el problema del taller de flujo (flowshop …...instituto tecnolÓgico de informÁtica. grupo de...

INSTITUTO TECNOLOacuteGICO DE INFORMAacuteTICA GRUPO DE SISTEMAS DE OPTIMIZACIOacuteN APLICADA UNIVERSITAT POLITEgraveCNICA DE VALEgraveNCIA

EL PROBLEMA DEL TALLER DE FLUJO (FLOWSHOP

SCHEDULING PROBLEM)Rubeacuten Ruiz

httpsoaities

1 Introduction2 Flowtime heuristics3 Flowtime local search4 Back to mathematical modeling5 Hybrid flowshops6 Conclusions

Contents

httpsoaities

bull Scheduling is a very active topic of research in operationsresearch

bull SciVal Trends Top 50 keyphrases by relevance based on111262 publications in the field of Management Scienceand Operations Research from 2009 to 2018

1 Introduction

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bull A flowshop is a very common productionlayout

bull In a flowshop there are n jobs that have to beprocessed in the same order in m machines

bull A job is then comprised of m tasks one per machine

bull A machine cannot process more than one job at the same time and one job cannot be processed by more than one machine at the same time

1 Introduction

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bull Each job needs a non-negative processing timeat each machine denoted by pij

bull Usually job passing is not allowed frommachine to machine permutation flowshopproblem

bull The most common objective is theminimization of the maximum completion timeor makespan

1 Introduction

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bull The flowshop with makespan criterion isalready an NP-Hard problem for mge3

1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

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bull Makespan maximizes machine utilization

bull Minimizing the sum of jobrsquos completion timesminimizes WIP and maximizes throughput

bull In practice total flowtime is a more realisticobjective

1 Introduction

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1 IntroductionBest Makespan 451

Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

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Time

Job 2 Job 3 Job 5Job 4Job 1

C3=306 C4=386

C5=443C2=449

C1=451=Cmax

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1 IntroductionWorst Makespan 522Best Flowtime 1464

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

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C1=88 C4=304 C5=395C2=155 C3=522=Cmax

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bull More than 40 papers that specifically proposeheuristics for the flowtime PFSP

bull Framinan et al (2005) propose aclassification between simple and compositemethods

bull Only the highest performing methods areevaluated in the computational comparison

2 Flowtime heuristics

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bull CDS of Campbell et al (1970)

bull MINIT MICOT and MINIMAX of Gupta (1972)

bull Krone and Steiglitz (1974)

bull Miyazaki et al (1978)

bull Miyazaki and Nishiyama (1980)

bull Ho and Chang (1991)

bull Rajendran and Chaudhuri (1991 1992)

bull Raj of Rajendran (1993)

bull Ho (1995)

bull LIT SPD1 and SPD2 of Wang et al (1997)

bull RZ of Rajendran and Ziegler (1997)

bull WY of Woo and Yim (1998)


httpsoaities

bull LR(x) LR(x)-FBE and LR(x)-BPE of Liu and Reeves (2001)

bull NEH-Flowtime of Framinan et al (2002)

bull IH1-IH7 of Allahverdi and Aldowaisan (2002)

bull B5FT of Framinan et al (2003)

bull FL and IH7-FL of Framinan and Leisten (2003)

bull C1-FL and C2-FL of Framinan et al (2005)

bull RZ-LW of Li and Wu (2005)

bull ECH1 and ECH2 of Li and Wang (2006)

bull IC1-IC3 of Li et al (2009)

bull FL-LS of Laha and Sarin (2009)


httpsoaities

bull NEH of Nawaz et al (1983) a very capableheuristic for the FPSP mainly for makespancriterion

bull LR(x) of Liu and Reeves (2001) very powerfulfor flowtime criterion

bull Simple idea Why not combining them


httpsoaities

2 Flowtime heuristicsProcedure LR-NEH(x)

Generate a job sequence 21 nαααα = by ascending 0jξ value (break ties according to ascending 0jIT value)

for 1=l to x do (generate x sequences)

ll απ = lJU αminus=

for 2=k to d do (construct a partial sequence with d jobs)

Take the job j with minimum kj ξ value (break ties according to minimum kjIT value) from U and place it at

the end of lπ Remove job j from U

endfor

(NEH heuristic)

Generate a partial sequence 21 dnminus= ββββ ( Uj isinβ dnj minus= 21 ) by ascending order of total

processing times

for 1=k to dn minus do (construct a complete sequence)

Take job kβ from β and insert it in all the dk + possible positions of lπ

Place job kβ in lπ at the tested position resulting in the lowest total flowtime

endfor

endfor

return the sequence 21 lππππ isin with the minimum total flowtime

Procedure LR-NEH( x)

Generate a job sequence by ascending value (break ties according to ascending value)

for to do (generate sequences)

for to do (construct a partial sequence with jobs)

Take the job with minimum value (break ties according to minimum value) from and place it at the end of Remove job from
endfor

(NEH heuristic)

Generate a partial sequence ( ) by ascending order of total processing times

for to do (construct a complete sequence)

Take job from and insert it in all the possible positions of

Place job in at the tested position resulting in the lowest total flowtime
endfor

endfor

return the sequence with the minimum total flowtime

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httpsoaities

bull As with LR(x) LR-NEH(x) has the parameter x

bull It also has a parameter d which has been setto 3n4

bull We also propose other 4 compositeheuristics All of them start from LR-NEH(x)

bull Different combinations of the local searchscheme of Rajendran and Ziegler (1997)With accelerations and to optimality iRZ andVNS of Mladenovic and Hansen (1997)

2 Flowtime heuristics

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bull PR1(x)

bull Each one of the x solutions in LR-NEH(x)are improved by iRZ

bull PR2(x)

bull iRZ is substituted by a simple VNS basedon insertion and interchangeneighborhoods


httpsoaities

bull PR3(x)

bull Local search is composed by iRZ and twoNEH-like local searches

bull PR4(x)

bull Same as PR3(x) but iRZ is substituted bythe VNS

bull Essentially simple methods and local searchschemes


httpsoaities

bull We test 14 simple heuristics

1 Raj heuristic of Rajendran (1993)

2-4 LIT SPD1 and SPD2 heuristics by Wang et al (1997)

5 RZ heuristic of Rajendran and Ziegler (1997)

6 WY heuristic by Woo and Yim (1998)

7-9 LR(1) LR(nm) and LR(n) of Liu and Reeves (2001)

10 NEH heuristic modified by Framinan et al (2002)

11 FL heuristic of Framinan and Leisten (2003)

12 RZ-LW heuristic of Li and Wu (2005)

13 FL-LS heuristic by Laha and Sarin (2009)

14 Proposed LR-NEH(x) heuristic


httpsoaities

bull And 13 composite heuristics

15-16 LR-FPE and LR-BPE of Liu and Reeves (2001)

17 IH7 heuristic of Allahverdi and Aldowaisan (2002)

18 IH7-FL heuristic of Framinan and Leisten (2003)

19-20 Composite heuristics C1-FL and C2-FL of Framinan et al(2005)

21-23 IC1 IC2 IC3 heuristics of Li et al (2009)

24-27 The presented composite heuristics PR1(x) PR2(x)PR3(x) and PR4(x)


httpsoaities

bull Other methods (especially the oldest ones) wereshown in previous studies to be clearly worse thanother tested methods

bull Accelerations and flowtime computing method of Liet al (2006) employed to save computational time

bull 120 instances of Taillard (1993)

bull n=20 50 100 times m=51020

bull n=200 times m=1020 and n=500 times m=20

bull Average relative percentage improvement frombest solution known as a response measure (RPI)


httpsoaities

bull All algorithms coded in C++

bull Runs on a cluster of 30 blade servers each one withtwo Intel XEON E5420 processors running at 25GHz and with 16 GB of RAM memory

bull All methods are deterministic However 5 differentruns are carried out in order to better estimate theCPU time

bull Our tested methods LR-NEH(x) PR1(x)-PR4(x) aretested with three values of x = 5 10 and 15

bull Therefore 37 algorithms times 5 replicates times 120instances =22200 results


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2 Flowtime heuristics Algorithm RPI Time Type PARETO Algorithm RPI Time Type PARETO

1 PR1(15) 033 2093 Composite 0 20 RZ-LW 129 1038 Simple 1

2 PR2(15) 036 1756 Composite 0 21 IH7-FL 130 8606 Composite 18

3 PR1(10) 039 2012 Composite 1 22 IH7 143 8745 Composite 19

4 PR2(10) 041 1702 Composite 1 23 C1-FL 172 6398 Composite 17

5 PR4(15) 041 1664 Composite 0 24 LR-NEH(15) 172 494 Simple 0



8 PR3(10) 046 1731 Composite 3 27 FL 199 6124 Simple 20

9 PR1(5) 050 1753 Composite 5 28 LR(n) 209 13412 Simple 26

10 PR3(5) 051 1458 Composite 0 29 LR(nm) 229 681 Simple 3

11 PR2(5) 051 1404 Composite 0 30 RZ 265 094 Simple 0

12 PR4(5) 053 1332 Composite 0 31 WY 283 4190 Simple 22

13 IC3 062 7725 Composite 12 32 LR(1) 313 029 Simple 0

14 IC2 066 1995 Composite 10 33 NEH 403 037 Simple 1

15 IC1 081 1441 Composite 2 34 Raj 502 008 Simple 0

16 C2-FL 095 13822 Composite 15 35 LIT 826 142 Simple 4

17 LR-FPE 114 1035 Composite 0 36 SPD2 1656 143 Simple 5

18 FL-LS 122 12024 Simple 16 37 SPD1 1737 118 Simple 4

19 LR-BPE 123 1134 Composite 1

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PR1(15)PR2(15)PR1(10)PR2(10)PR4(15)PR3(15)PR4(10)PR3(10)PR1(5)PR3(5)PR2(5)PR4(5)

ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL

LR_NEH(15)LR_NEH(10)LR_NEH(5)

FL

LR(n)

LR(nm)RZ

WY

LR(1)NEHRajLIT SPD2 SPD1

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

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2 Flowtime heuristicsPR1(15)

PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

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2 Flowtime heuristicsPR

1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities

bull Our presented methods range from fast andhigh performance simple heuristics LR-NEH(x)to slower but with state-of-the-art performance

bull PR1(5) results in 05 deviation from bestknown solutions in less than 18 seconds onaverage (less than 3 seconds for instances upto 100 jobs and 20 machines)


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bull Can we improve the results further

bull Most proposed methods are fairly complex

bull To propose simple and easy to implement newstate-of-the-art methods for the problem

bull To carry out a comprehensive computationalstudy for the problem

3 Flowtime local search

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bull We are interested in simple approaches

bull Iterated local Search (ILS) of Lourenccedilo et al(2003) and Iterated Greedy (IG) of Ruiz andStuumltzle (2007) have shown competitiveresults in similar settings

bull We also present population extensions ofboth approaches


httpsoaities


procedure ILS ionitialSolutGenerateInlarr0π

)( 0ππ hLocalSearclarr Local search repeat

)( ππ onPerturbatilarr Perturbation of the local optimum )( ππ hLocalSearclarr Local search

)( πππ erionAcceptcritlarr Decide if new solution replaces the incumbent until termination criterion met

end

procedure ILS

Local search
repeat

Perturbation of the local optimum
Local search
Decide if new solution replaces the incumbent
until termination criterion met

end

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httpsoaities

bull INITIAL SOLUTION We employ the veryefficient heuristic LR(nm) of Li et al (2009)and Zhang et al (2009) This is an extensionof the LR(x) heuristic of Liu and Reeves(2001)

bull LOCAL SEARCH We employ the RZprocedure of Rajendran and Ziegler (1997)With accelerations and to optimality iRZ

3 Flowtime local search

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bull PERTURBATION A given number γ of randominsertion moves

bull ACCEPTANCE CRITERION Simulatedannealing-like with constant temperaturefactor λ as done by Stuumltzle (1998) or Ruizand Stuumltzle (2007 2008) and others


httpsoaities

3 Flowtime local searchprocedure the presented ILS algorithm

Set the parameters γ and λ

)(0 mnLRlarrπ Generate an initial solution

)( 0ππ iRZlarr Local search

ππ larr Best solution found so far repeat

)( ππ onPerturbatilarr Perturbation of the local optimum )( ππ iRZlarr Local search

if sumsum lt )()( ππ jj CC then Acceptance criterion

ππ larr Accept if better than incumbent if sumsum lt )()( ππ jj CC then check if new best solution

ππ larr endif

elseif ))()(exp()( eTemperaturCCrand jj sumsum minusle ππ then

ππ larr Simulated annealing acceptance criterion endif

until termination criterion is met end

procedure the presented ILS algorithm

Set the parameters and
Generate an initial solution
Local search
Best solution found so far
repeat

Perturbation of the local optimum
Local search
if then Acceptance criterion
Accept if better than incumbent
if then check if new best solution

endif

elseif then
Simulated annealing acceptance criterion
endif

until termination criterion is met

end

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httpsoaities


procedure IGA tionitialSouluGenerateInlarr0π Generate an initial solution

)( 0ππ hLocalSearclarr Local search repeat

)(_ ππ onConstructinDestructiolarr Destruction and construction )( ππ hLocalSearclarr Local search

)( πππ erionAcceptcritlarr Decide if new solution replaces the incumbent until termination criterion is met

end

procedure IGA

Generate an initial solution
Local search
repeat

Destruction and construction
Local search

end

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httpsoaities

bull INITIAL SOLUTION LOCAL SEARCH andACCEPTANCE CRITERION do not change

bull DESTRUCTION_CONSTRUCTION Identical toRuiz and Stuumltzle (2007) d jobs are randomlyselected and extracted Then they areinserted one by one in all positions of thesequence (as in the NEH heuristic)


httpsoaities

bull POPULATION VARIANTS pILS and pIGA

bull Initial population of size x using LR(x)

bull At each generation one solution from thepopulation is selected

bull 50 of the times using binary tournamentwith flowtime value

bull 50 of the times using inverted binarytournament with the age of the solution


httpsoaities

bull GENERATIONAL SCHEME

bull A new solution replaces the worst solution ofthe population iff

1 Flowtime value better than that of the worst

2 There is no other identical solution in thepopulation (permutation)

3 The average diversity value of the populationdoes not decrease (Pan and Ruiz 2011)


httpsoaities

bull DIVERSITY CALCULATION


[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ

sequence theof position at appears job timesofnumber

ijji =φ

jjjj

prime

=

jobafter y inmediatel appears job timesofnumber λ

httpsoaities

bull α and β are the number of elements that arelarger than zero in both matricesrespectively

bull Then the diversity is calculated as


2)11min()1(

)1()1min(

minusminustimesminus

minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities

bull We test 16 different algorithms1 Discrete Differential Evolution DDERLS of of Pan et al (2008)

2 Iterated Greedy IGRLS of Pan et al (2008)

3 Estimation of Distribution EDAJ of Jarboui et al (2009)

4 Variable neighborhood search VNSJ of Jarboui et al (2009)

5 Iterated local search ILSD of Dong et al (2009)

6 Hybrid genetic algorithm HGAT1 of Tseng and Lin (2009)

7 Hybrid genetic algorithm HGAZ of Zhang et al (2009)


9 Genetic Local Search AGA of Xu et al (2011)

10 Hybrid Discrete Differential Evolution hDDE of Tasgetiren et al (2011)

11 Discrete Ant Bee Colony DABC of Tasgetiren et al (2011)

12 Iterated Greedy SLS of Dubois-Lacoste et al (2011)

13-16 Proposed ILS IGA pILS and pIGA


httpsoaities

bull 120 instances of Taillard (1993)

bull n=20 50 100timesm=51020

bull n=200timesm=1020 and n=500timesm=20

bull We add 30 more instances with the missingn=200timesm=5 and n=500timesm=510

bull Average relative percentage deviation from bestsolution known as a response measure (AVRPD)

bull All algorithms coded in C++ and run 5 times oneach instance during milliseconds elapsedCPU time on Intel XEON E5420 processors runningat 25 GHz and with 16 GB of RAM memory


mnt ρ=

httpsoaities

3 Flowtime local searchρ=30

IGRLS DDERLS EDAJ VNSJ ILSD HGAT1 HGAZ HGAT2

AVRPD 039 039 772 488 049 223 074 529

AGA hDDE DABC SLS IGA pIGA ILS pILSAVRPD 087 064 083 041 024 028 025 031

ρ=60IGRLS DDERLS EDAJ VNSJ ILSD HGAT1 HGAZ HGAT2

AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities

3 Flowtime local searchInteractions and 950 Percent Tukey HSD Intervals

015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities

bull We have studied the permutation flowshopscheduling problem with total flowtime criterion

bull We have proposed four simple methods basedon local search Iterated Greedy and IteratedLocal Search

bull We have carried out a comprehensivecomparison against 12 other methods

bull IGA and ILS are state-of-the-art methods


httpsoaities

bull IGA and ILS better than other much morecomplex algorithms

bull pIGA and pILS also good but not better thanthe simpler non population variants

bull Future work

bull Sequence dependent setup times andflowtime objective seldom studied

bull Earliness-Tardiness objectives

bull Hybrid flowshops


httpsoaities

bull MIP models have been gradually abandonedand have given way to heuristics and mostnotably metaheuristics

bull However solvers keep improving Accordingto Bixby (2017 ECCO conference) since1991 solvers are now 13 million times faster(accumulated) not considering hardwareimprovements

4 Back to mathematical modeling

httpsoaities

bull Constraint Programming (CP) is gainingtraction in scheduling as of late (Bukchin andRaviv 2018 Laborie et al 2018)

bull CP models are notorious for their ability to findinteger solutions

bull However classical CP lacks boundingmechanisms and therefore does not provideoptimality guarantees or gaps

bull Since CPLEX 128 CP Optimizer guaranteesbounds and optimality GAPs for any integersolution found


httpsoaities

bull How do modern solvers and formulationsfare for different scheduling problems

bull How does CP Optimizer compare with aregular MIP solver

bull A exact approach renaissance forscheduling problems


httpsoaities

bull Manne (1960) MIP


httpsoaities

bull CP Optimizer code


httpsoaities

bull We use Taillardrsquos (1993) benchmark (120 instances) as wellas Vallada Ruiz and Framinan (2015) benchmark with 240large instances (up to 800 jobs and 60 machines)

bull CPLEX 128 + Python 366

bull Cluster of 200 virtual machines with 2 virtual processorsand 8 GBytes of RAM memory each The virtual machinesrun Windows 10 Enterprise 64 bits Virtual machines arerun in an OpenStack virtualization platform supported by12 blades each one with four 12-core AMD Opteron AbuDhabi 6344 processors running at 26 GHz and 256 GB ofRAM for a total of 576 cores and 3 TBytes of RAM


httpsoaities

bull CP never runs out of memory and always finds asolution

No Solution Out of memoryCP 0 0

Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities

bull CP still not competitive with metaheuristics (lt03RPD)

Average GAP Average RPDCP 23168 811Taillard

600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080

MIP 36142 1273Taillard

600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities

bull We have tested the following problems

bull Non-permutation flowshop with makespan criterion

bull No-wait flowshop with makespan criterion

bull Sequence-dependent setup times flowshop withmakespan criterion

bull Flowshop with Total Completion Time criterion

bull Distributed flowshop with makespan criterion

bull Hybrid flowshop with makespan criterion

bull Each problem with its own benchmark


httpsoaities

bull Non-permutation flowshop with makespan criterionAverage GAP No Solution Out of memory

CP 22027 0 0Taillard

600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0

MIP 56102 122 422Taillard

600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities

bull No-wait flowshop with makespan criterionAverage GAP No Solution Out of memory


600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities

bull Sequence-dependent setup times flowshop withmakespan criterion (480 instances)

Average GAP No Solution Out of memoryCP 5032 0 0

600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities

bull Flowshop with Total Completion Time criterion(360 instances)


600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities

bull Distributed flowshop with makespan criterion (600instances)


600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities

bull Hybrid flowshop with makespan criterion (1440instances)


600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities

bull CP is vastly superior to the best combination ofMIP model + state-of-the-art solver

bull CP gives an integer solution in all cases

bull CP does not show out of memory problems

bull Greatly reduced relative percentage deviationsand GAP values in most scenarios

bull CP still not competitive with state-of-the-artmetaheuristics but getting somewhat close insome cases


httpsoaities

bull Companies still not using finite capacityschedulers for production programming in mostcases

bull Trend to address more realistic problems

5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling

Dry grinding Wetting Kneading Extrusion

Spray drying Molding Drying

Single fast firing

1st fast firing

Single slow firing

2nd fast firingGlazing

Glaze preparation

1st slow firing

Classification and packing

httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and

grindingSpray drying Molding Drying

Glaze preparation

Single kiln firingGlazing

Selection and

packing

httpsoaities

bull We deal with hybrid flexible flowshop problemsbull A set N of jobs N=1hellipn that have to be processed on a

set M of stages M=1hellipmbull At each stage we have a set Mi=1hellipmi of mi unrelated

parallel machinesbull All jobs are processed sequentially on the stagesbull pilj is the processing time of job j at machine l inside stage i

5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities

bull We consider many realistic constraintsbull Fj denotes the set of stages that job j visitsbull Eij is the set of machines that can process job j at stage ibull rmil represents the release date of machine l inside stage

i No job can start processing on this machine before thisrelease date

bull Pj is the set of jobs that should precede job j The firstoperation of job j should wait until all last operations ofjobs in Pj have finished

5 Hybrid flowshops

httpsoaities

bull Siljk is the machine based setup times on machine l atstage i when processing job k after having processed jobj

bull Setups might be either anticipatory or non-anticipatorybull Ailjk=0 -gt the setup is non-anticipatory and one must wait for

job j to arrive at machine l before carrying out the setupbull Ailjk=1 -gt the setup can be done as soon as machine l is free

5 Hybrid flowshops

httpsoaities

bull lagilj is the time lag between the end of job j at machine linside stage i and the beginning of the next stage in whichjob j is processed

bull If lagiljlt0 then overlapping occurs (not all parts in job j needto be finished at stage i before processing at the next stagestarts)

bull If lagiljgt0 then we have a waiting time between stages

5 Hybrid flowshops

httpsoaities

bull We will consider the common makespan criterioninitially

bull The problem is NP-Hard since many simplificationsof it are NP-Hard

bull Following the common three field notation andVignier et al (1999) the problem can be denotedas

max)(

1)( ))(( CprecMSlagrmRMHFFLm jijk

mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities

bull We extend the problem with theconsideration of due dates

bull Cj is the completion time of job j at the shop

bull dj is the due date of job j

bull wj its importance or priority

bull Tj=max0 Cj - dj is the tardiness of job j

bull Ej=max0 dj - Cj is the earliness of job j

5 Hybrid flowshops

httpsoaities

bull Extension of the due date concept to due datewindows

5 Hybrid flowshops

djCj

0

dj- +

httpsoaities

bull Considered objective function

5 Hybrid flowshops

httpsoaities

bull Literature on hybrid flowshop very rich

bull This objective has not been studied yet

bull Objectives of the research

bull To propose simple methods

bull To compare them against the best adaptedalgorithms from the literature

bull State-of-the-art results

5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

bull We propose an Iterated Local searchprocedure

bull Very simple

httpsoaities

5 Hybrid flowshops

bull Solution representation is a complex issue inHFS

bull A simple permutation not enough

bull Complex representations too time consuming

bull Simple permutation with the FAM rule

bull For stage 2hellipm jobs are sorted according totheir completion times in the previous stage

httpsoaities

5 Hybrid flowshops

bull Active schedules not enough to optimizeearliness

bull We apply an idle time insertion method to alljobs in the last machine

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99

d1 d6d1 + d2 d2 + - d3 d3 - + d4 d4 - + d5 d5 - + d6 d7 d7 d8 d8 - + - + - +

5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops

bull We apply a two stage local search

bull The first one works with the permutation(insertion and interchange inside VND)

bull A second local search is carried out over theexact representation

bull But only a few promising neighbors areexplored

httpsoaities

5 Hybrid flowshops

bull Simple perturbation by carrying out anumber of insertion and interchanges

bull Directed perturbation A number of perturbedsolutions is generated and the best isobtained

bull Tournament acceptance criterionbull List with the best found solutions

bull If a better solution is found the list is cleared

bull If solution not better tournament select a solution fromthe list

httpsoaities

5 Hybrid flowshops

bull We also present an Iterated Greedy (IG)procedure based on the work of Ruiz andStuumltzle (2007) for the regular flowshop

bull Straight adaptation where we apply the samelocal search in two stages idle time insertiontournament acceptance criterion

httpsoaities

5 Hybrid flowshops

bull Calibration by means of DOE+ANOVA

ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities

bull We test the proposed ILS and IG against the 9 bestexisting methods from the literature

1 The Artificial Immune System of Engin and Doumlyen (2004) (AIS)

2 The GA of Ruiz and Maroto (2006) (GAR)

3 The Ant Colony Optimization of Alaykyacuteran et al (2007) (ACO)

4 The GA of Kahraman et al (2008) (GAK)

5 The improved SA of Naderi et al (2009) (HSA)

6 The ACO of Khalouli et al (2010) (ACOK)

7 The ILS of Naderi et al (2010) (ILSN)

8 The Discrete Colonial Competitive Algorithm of Behnamian andZandieh (2011) (DDCA)

9 The Artificial Bee Colony of Pan et al (2013) (ABCP)

5 Hybrid flowshops

httpsoaities

bull All algorithms coded in C++

bull Competing algorithms carefully reimplemented

bull All methods calibrated with ANOVA

bull All methods include the proposed idle time insertionprocedure

bull Runs on a cluster of 30 blade servers each one withtwo Intel XEON E5420 processors running at 25GHz and with 16 GB of RAM memory

bull 342 days of computer time for calibration

bull Calibration instances different from test instances

5 Hybrid flowshops

httpsoaities

bull Two sets of instances

bull 1620 small instances with up to 20 jobs 3 stagesand 4 machines per stage

bull 1400 large instances with up to 200 jobs 10stages and 10 machines per stage

bull Average relative deviation index from bestsolution known (RDI)

bull 3 different stopping times t= ρmiddotnmiddotmmiddot millisecondswhere ρ is tested at 3 levels 30 60 and 90

5 Hybrid flowshops

httpsoaities

bull We test ILS and IG with and without Tournamentacceptance criterion (ILS ILST IG IGT)

bull 5 replicates per algorithm and instance

bull Therefore 13 algorithms times 3 stopping times times 5replicates times (1620+1440) instances =596700results

bull 193 days of computer time for tests

5 Hybrid flowshops

httpsoaities

ρ ABCP ACO ACOK AIS DCCA GAK GAR HSA ILSN IG IGT ILS ILST

30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025

5 Hybrid flowshopsρ ABCP ACO ACOK AIS DCCA GAK GAR HSA ILSN IG IGT ILS ILST

30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

HSA IG IGT ILS ILST014

018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities

bull We have studied the hybrid flowshop problemwith a generalized objective function whichminimizes the earliness and tardiness from adue date window

bull We have presented simple local searchmethods

bull Two stage local search with a limited localsearch in the exact representation key toresults

5 Hybrid flowshops

httpsoaities

bull Comprehensive comparison against 9 adaptedand calibrated methods

bull Results are clearly state-of-the-art in all testedscenarios under small and large instances

bull Future work

bull More realistic considerations like non-identical machines per stage or sequence-dependent setup times

5 Hybrid flowshops

httpsoaities

bull Although we have considered a highly realisticproblem there are still a number of assumptions

bull No errors in the processing of jobs

bull No breakdowns and continuous machine availability

bull Unlimited buffer capacity in-between stages

bull Not considered Recirculation preemption no wait hellip

bull Heuristics metaheuristics need to be developed

5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

bull Flowshops problems have many applications inpractice

bull There are many variants in objectivesconstraints and settings

bull Simple methods usually show goodperformance

bull Lot of work to do

6 Conclusions




El Problema del taller de flujo (FLOWSHop scheduling problem)


1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

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5 Hybrid flowshops

6 Conclusions


httpsoaities


Contents

httpsoaities



1 Introduction

httpsoaities





1 Introduction

httpsoaities




1 Introduction

httpsoaities


1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





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endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


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l

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k

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x

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k

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b

b

b

b

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j

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b

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d

n

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=

k

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d

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k

b

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b

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d

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+

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l

p

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j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





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end

procedure ILS

Local search
repeat

Local search

end

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p

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not

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not

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(

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not

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httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

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0

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n

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not

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p

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p

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not

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httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

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image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

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not

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GenerateIn

not

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not

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httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






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httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



1 Introduction

httpsoaities





1 Introduction

httpsoaities




1 Introduction

httpsoaities


1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





1 Introduction

httpsoaities




1 Introduction

httpsoaities


1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




1 Introduction

httpsoaities


1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


1 Introduction

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




1 Introduction

httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


Worst Flowtime 2035

52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

Time


C3=306 C4=386

C5=443C2=449

C1=451=Cmax

httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


52547542537532527522517512575250

Machine 1

Machine 2

Machine 3

Machine 4

Time


1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

C1=88 C4=304 C5=395C2=155 C3=522=Cmax

httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities









bull Ho (1995)





httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities












httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities








endfor

(NEH heuristic)


processing times




endfor

endfor






endfor

(NEH heuristic)




endfor

endfor


oleObject2bin

image3wmf

0

j

IT

oleObject3bin

image4wmf

1

=

l

oleObject4bin

image5wmf

x

oleObject5bin

image6wmf

x

oleObject6bin

image7wmf

l

l

a

p

=

oleObject7bin

image8wmf

l

J

U

a

-

=

oleObject8bin

image9wmf

2

=

k

oleObject9bin

image10wmf

d

oleObject10bin

image11wmf

d

oleObject11bin

image12wmf

j

oleObject12bin

image13wmf

k

j

x

oleObject13bin

image14wmf

k

j

IT

oleObject14bin

image15wmf

U

oleObject15bin

image16wmf

l

p

oleObject16bin

image17wmf

j

oleObject17bin

image18wmf

U

oleObject18bin

image19wmf

2

1

d

n

-

=

b

b

b

b

oleObject19bin

image20wmf

U

j

Icirc

b

oleObject20bin

image21wmf

d

n

j

-

=

2

1

oleObject21bin

image22wmf

1

=

k

oleObject22bin

image23wmf

d

n

-

oleObject23bin

image24wmf

k

b

oleObject24bin

image25wmf

b

oleObject25bin

image26wmf

d

k

+

oleObject26bin

image27wmf

l

p

oleObject27bin

image28wmf

k

b

oleObject28bin

image29wmf

l

p

oleObject29bin

image30wmf

2

1

l

p

p

p

p

Icirc

oleObject30bin

image1wmf

2

1

n

a

a

a

a

=

oleObject1bin

image2wmf

0

j

x

httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

bull PR1(x)


bull PR2(x)



httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

bull PR3(x)


bull PR4(x)




httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities













httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities









httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




bull n=20 50 100 times m=51020




httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





















httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



ICH3

ICH2ICH1

C2_FL

LR_FPE

FL_LS

LR_BPERZ_LW

IH7_FLIH7

C1_FL


FL

LR(n)

LR(nm)RZ

WY


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

CPU

Tim

e

RPI

httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


PR2(15)

PR1(10)

PR2(10)PR4(15)

PR3(15)

PR4(10)

PR3(10)

PR1(5)

PR3(5)

PR2(5)PR4(5)

IC2

IC1

LR-FPELR-BPE

RZ-LW

LR-NEH(15)

LR-NEH(10)

LR-NEH(5)

LR(nm)

RZLR(1) NEH Raj

0

5

10

15

20

0 1 2 3 4 5

CPU

Tim

e

RPI

httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


1(15

)

PR2(

15)

PR1(

10)

PR2(

10)

PR4(

15)

PR3(

15)

PR4(

10)

PR3(

10)

PR1(

5)

PR3(

5)

PR2(

5)

PR4(

5)

IC3

IC2

IC1

C2-

FL

LR-F

PE

FL-L

S

LR-B

PE

RZ-

LW

IH7-

FL IH7

C1-

FL

LR-N

EH(1

5)

LR-N

EH(1

0)

LR-N

EH(5

)

FL

LR(n

)

LR(n

m)

RZ

WY

025

05

075

1

125

15

175

2

225

25

275

3

RPI

httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






end

procedure ILS

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

p

p

on

Perturbati

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

ion

itialSolut

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

oleObject11bin

image12wmf

)

)

(

)

(

exp(

)

(

e

Temperatur

C

C

rand

j

j

aring

aring

-

pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

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p

p

on

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not

oleObject6bin

image7wmf

)

(

p

p

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not

oleObject7bin

image8wmf

aring

aring

lt

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(

)

(

p

p

j

j

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oleObject8bin

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p

not

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(

)

(

p

p

j

j

C

C

oleObject10bin

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p

p

not

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(

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(

exp(

)

(

e

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rand

j

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pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

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not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities









ππ larr endif





Local search
repeat

Local search

endif

elseif then
endif


end

oleObject2bin

image3wmf

)

(

0

m

n

LR

not

p

oleObject3bin

image4wmf

)

(

0

p

p

iRZ

not

oleObject4bin

image5wmf

p

p

not

oleObject5bin

image6wmf

)

(

p

p

on

Perturbati

not

oleObject6bin

image7wmf

)

(

p

p

iRZ

not

oleObject7bin

image8wmf

aring

aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject8bin

image9wmf

p

p

not

oleObject9bin

image10wmf

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aring

lt

)

(

)

(

p

p

j

j

C

C

oleObject10bin

image11wmf

p

p

not

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(

)

(

exp(

)

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e

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C

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j

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pound

p

p

oleObject12bin

image13wmf

p

p

not

oleObject13bin

image1wmf

g

oleObject1bin

image2wmf

l

httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






end

procedure IGA

Local search
repeat

Local search

end

oleObject2bin

image3wmf

)

(

_

p

p

on

Constructi

n

Destructio

not

oleObject3bin

image4wmf

)

(

p

p

h

LocalSearc

not

oleObject4bin

image5wmf

)

(

p

p

p

erion

Acceptcrit

not

oleObject5bin

image1wmf

tion

itialSoulu

GenerateIn

not

0

p

oleObject1bin

image2wmf

)

(

0

p

p

h

LocalSearc

not

httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



[ ]

=times

nnnn

n

n

nnji

21

22212

12111

φφφ

φφφφφφ

φ

[ ]

minus

minusminus

=times

21

212

121

nn

n

n

nnjj

λλ

λλλλ

λ


ijji =φ

jjjj

prime

=


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




2)11min()1(

)1()1min(


minusminus+

minustimesminus

=xnn

nxnn

ndiv βα

httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities















httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


bull n=20 50 100timesm=51020






mnt ρ=

httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



AVRPD 039 039 772 488 049 223 074 529



AVRPD 036 036 702 439 049 213 063 450



AVRPD 035 034 664 417 050 209 059 409


42 Better

httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


015

035

055

075

095

AVR

PD

IGAILS

pIGApILS

DDERLS

IGRLS

SLSILSD

hDDEHGAZ

DABCAGA

ρ

30

60

90

httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



bull Future work





httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



Taillard600 0 0

1800 0 03600 0 0

VRF600 0 0

1800 0 03600 0 0

MIP 642 (297) 187 (83)Taillard

600 40 01800 40 03600 34 0

VRF600 229 11

1800 166 733600 133 103


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 686 3621800 609 2913600 566 253

VRF600 74924 1704

1800 41681 11793600 20543 1080


600 34550 8021800 31581 6113600 30532 574

VRF600 -- --

1800 41725 20843600 42322 2296


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities










httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 740 0 01800 663 0 03600 617 0 0

VRF600 74116 0 0

1800 39291 0 03600 16734 0 0


600 55838 7 31800 53428 0 103600 52005 0 10

VRF600 59287 111 59

1800 59545 4 1683600 56510 0 172


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 27031 0 01800 5610 0 03600 5543 0 0

VRF600 257211 0 0

1800 141131 0 03600 89713 0 0


600 118940 0 01800 109397 0 03600 104093 0 0

VRF600 242346 107 10

1800 222293 107 103600 207732 98 10


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 5157 0 01800 5009 0 03600 4928 0 0

MIP 124442 23 28600 131461 11 0

1800 129140 7 03600 112725 5 28


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 70226 0 13600 41198 0 9

MIP 29593 404 138600 30880 266 14

3600 28306 138 124


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 19743 0 01800 19162 0 03600 19367 0 0

MIP 18781 516 119600 19977 234 20

1800 16617 131 503600 19749 151 49


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



600 28491 0 01800 27954 0 03600 28130 0 0

MIP 114433 1263 0600 126879 521 0

1800 100786 314 03600 115633 428 0


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



5 Hybrid flowshops

httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

62 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

63 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

64 Maacutester-UPV

5 Hybrid flowshops

httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

65 Maacutester-UPV

5 Hybrid flowshops

Raw materials

preparation

Wet milling



Single fast firing

1st fast firing

Single slow firing


Glaze preparation

1st slow firing


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

66 Maacutester-UPV

5 Hybrid flowshops

Raw Materials

preparation

Milling and


Glaze preparation


Selection and

packing

httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops

1

2

l

1

2

3

3

4

4

C11 = 4

5

1

2

1

i

2

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12

C12 = 3

C14 = 6

C13 = 9

C15 = 7

5

C22 = 7

C24 = 8

C25 = 12

C23 = 10C21 = 9

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




5 Hybrid flowshops

httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




5 Hybrid flowshops

httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




max)(


mi

i=

5 Hybrid flowshops

httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

1

2

1

2

1

1

2

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Rm11

4

1

14

Rm12

3

Rm21

Rm22

Rm31

8

16

23

2

12

2

21lag122

24lag111

1

3214

1

28 34lag221

S2123

27

li

3

36

S3113

40

3

48

S1224

42 48

S1115

44 48

4

58

4

6059 6658

S3134

lag124

5

59

5

lag11554

S2215

48 66

S3145

72 74

5lag225

77

10

59

lag21336 39

Cmax=77

5 Hybrid flowshops

httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

Job 2 Time

Machine 1

Machine 2

Machine 3

Machine 4

Stage 1

Stage 3

Job 3Job 1

Stage 2

Machine 5

Setup Release dates

Cmax

5 Hybrid flowshops

httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

t5ms25ms125ms

3

6

9

12

SRIS IG ILS MA GA

5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







5 Hybrid flowshops

httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


5 Hybrid flowshops

djCj

0

dj- +

httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops


bull Very simple

httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops



1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 856 61 65 69 75 82 84 86 92 9793

1 2 3 4

62 64 67 68 70 72 74 76 79 81 88 90 93 95 97 99


5 6 7 857 62 66 70 76 83 86 88 9894

httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops





httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops






httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops



httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops


ϖ

24

29

34

39

44

49

54

Rel

ativ

e D

evia

tion

Inde

x (R

DI)

1 10 30 50

ω

3

loopmax

100 200 300

2LS

1 2 3 4d

012 1

httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities











5 Hybrid flowshops

httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities








5 Hybrid flowshops

httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities






5 Hybrid flowshops

httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





5 Hybrid flowshops

httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities


30 170 818 9727 642 258 247 207 164 177 036 035 036 035

60 128 816 9582 597 249 208 148 089 099 023 022 025 023

90 107 815 9499 572 240 192 121 058 066 017 015 020 017

Average 135 817 9603 604 249 216 158 104 114 025 024 027 025


30 171 6998 6626 42 547 296 235 109 102 045 046 045 044

60 147 693 6099 37 491 272 204 096 094 033 035 034 034

90 137 688 5817 34 481 259 188 091 09 028 030 029 029

Average 152 694 6181 38 507 276 209 099 096 036 037 036 036

275 lower

433 lower

httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops

0

03

06

09

12

15

18

Rel

ativ

e D

evia

tion

Inde

x (R

DI)


018

022

026

03

034

038

IG IGT ILS ILST

ρ306090

httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities




5 Hybrid flowshops

httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities



bull Future work


5 Hybrid flowshops

httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities







5 Hybrid flowshops

httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

5 Hybrid flowshops

96 Maacutester-UPV

httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities

97 Maacutester-UPV

5 Hybrid flowshops

httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


httpsoaities





6 Conclusions






1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions







1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction

1 Introduction




















































5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

5 Hybrid flowshops

6 Conclusions


el problema del taller de flujo (flowshop …...instituto tecnolÓgico de informÁtica. grupo de...

Documents

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