mit msl pizzamodel (1)

8/13/2019 MIT MSL Pizzamodel (1)

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Randolph Kirchain and Frank R Field, Materials Systems Laboratory, Massachusetts Institute of Technology

PIZZA MAKING PROCESS-BASED COST MODEL

MIT - Materials Systems Laboratory

Jump to Sensitivity Analysis

PIZZA DESIGN

Pizza Thickness 8mmPizza Diameter 30cm

Pepperoni Thickness 0.25cm

Pepperoni Coverage 80%

Cheese Density 0.3g/cm2

Sauce Density 0.25g/cm2

EXOGENOUS DATA

Annual Production Volume 50(000/yr)

Facility Production Capacity 100(000/yr)

Product Life 5yrsDirect Wages (w/ benefits) $15.00 /hr

Working Days/Yr 240

Downtimes

No (i.e., none NOT No.) Operations 16hrs/dayPlanned Paid 0.5hrs/day

Planned Unpaid 1hrs/day

Discount Rate 10%

P i B ildi S $1 500 /


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Floor space 15m2Energy Consumption (baking) 240,000btu/h

Cooking Target Centerline Temperature 60C

Dough Temp 20COven Temp 225C

Direct Laborers Per Prep 1

Dedicated Equipment (1/0) 1(1=y;0=n)

Auxiliary Equip. Cost (% mmch) 50.0%

Installation Cost (% mmch) 20.0%Maintenance Cost (% invc) 5.0%

Overrides

Total Cycle Time 0 sec

Food Characteristics

Pepperoni Stick Length 60cmPepperoni Stick End Trim 1cmPepperoni Diameter 2.5cmPepperoni Cost $1.00 /stick

Dough Density 0.8g/cc

Dough Cost 0.25$ /kg 0.50$Dough Thermal Diffusivity 1.50E-08 0.5Cheese Cost $8 /kgSauce Cost $3 /kg


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PIZZA MAKING - COST SUMMARYMIT - Materials Systems Laboratory

VARIABLE COSTS per piece per year percentMaterial Cost $3.48 $173,963 63.96%

Energy Cost $0.08 $3,939 1.45%Labor Cost $0.42 $20,834 7.66%

Total Variable Cost $3.97 $198,736 73.07%

FIXED COSTS per piece per year percent

Main Machine Cost $0.63 $31,714 11.66%Auxiliary Equipment Cost $0.26 $13,214 4.86%

Tooling Cost $0.00 $237 0.09%

Fixed Overhead Cost $0.37 $18,314 6.73%

Building Cost $0.14 $7,160 2.63%

Maintenance Cost $0.05 $2,616 0.96%

Total Fixed Cost $1.47 $73,257 26.93%

Total Fabrication Cost $5.44 $271,992 100.00%

RELATED VARIABLES

Material Requirements:

Pizza Area 706.86 cm2

Pepperoni Area 565.49 cm2

P i Sti k 236 00 li / ti k


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Process Calculations

Effective Production Volume 50,506

Effective Capacity 101,011Capacity and Volume are Consistent? 1Available Operating Time 1,200 hours / year

Effective Cycle Time (from below) 90 secs / partRequired Operating Time (produced) 1,263 hours / yearRequired Operating Time (capacity) 2,525 hours / yearRun-Time for One Machine (produced 105%Run-Time for One Machine (capacity) 210%

Number of Parallel Streams 3.00

Paid Operating Time (available in year 1,320 hours / year

Actual Paid Operating Time (allocated 1,389 person-hours / year

Number of tools required 18

Required Building Space 45 sq m

Annual Energy Consumption 303 MMBtu

Cycle Time Calculations

Predicted Used

Cooking Time 150Total Cycle Time (sec) 180.0 180.0


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cp,potato = 3.64 kJ/kgK 3.64

kpotato = 0.55 W/mK 0.55

potato = 1.510-7

m2/s 3.00E-08

h = 400 W/m

2

K

Temp (x,t) 99.8318579

erf 0.610576303

Table for looking up cycle time99.8318579

10 20.00 1020 20.05344958 2030 20.58816814 3040 22.01377139 4050 24.28887419 5060 27.17807223 6070 30.44719926 70

80 33.91728038 8090 37.46430322 90

100 41.00644335 100110 44.49155806 110120 47.88761881 120130 51.17601605 130140 54.35 140

150 57.40 150160 60.32 160170 63.13 170180 65.83 180


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370 101.16 370380 102.45 380390 103.70 390400 104.91 400

410 106.09 410420 107.24 420430 108.35 430440 109.44 440450 110.49 450460 111.52 460470 112.52 470480 113.49 480

490 114.44 490500 115.37 500510 116.27 510520 117.15 520530 118.01 530540 118.8561345 540550 119.6780362 550

560 120.4813571 560570 121.2667774 570580 122.0349433 580590 122.7864694 590600 123.5219406 600610 124.2419137 610620 124.9469193 620

630 125.6374634 630640 126.3140285 640650 126.9770751 650660 127.6270432 660


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850 137.9576203 850860 138.4146877 860870 138.8646624 870880 139.307725 880890 139.7440498 890900 140.173805 900910 140.5971532 910920 141.0142511 920930 141.4252504 930940 141.8302977 940950 142.2295346 950960 142.6230981 960

970 143.0111208 970980 143.393731 980990 143.7710528 990

1000 144.1432066 10001010 144.5103087 10101020 144.872472 10201030 145.229806 1030

1040 145.5824165 10401050 145.9304064 10501060 146.2738754 10601070 146.6129202 10701080 146.9476347 10801090 147.27811 10901100 147.6044346 1100

1110 147.9266943 11101120 148.2449726 11201130 148.5593505 11301140 148.869907 1140


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PIZZA MAKING - Sensitivity AnMIT - Materials Systems Labo

Prod Volume Var. Cost Fixed Cost Total Cost$3.97 $1.47 $5.44

1 $3.98 $73.26 $77.235 $3.98 $14.65 $18.63

10 $3.98 $7.33 $11.30

15 $3.97 $4.88 $8.86

investment 20 $3.97 $3.66 $7.64

$270,000 25 $3.97 $2.93 $6.90$112,500 30 $3.97 $2.44 $6.42

$900 40 $3.97 $1.83 $5.81

50 $3.97 $1.47 $5.44

$67,500 60 $3.97 $1.22 $5.20

70 $3.97 $1.05 $5.02

$338,400 80 $3.97 $0.92 $4.8990 $3.97 $0.81 $4.79

100 $3.97 $0.73 $4.71

110 #N/A #N/A #N/A

120 #N/A #N/A #N/A130 #N/A #N/A #N/A

140 #N/A #N/A #N/A

150 #N/A #N/A #N/A

U it C t C it

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

$18.00

$20.00

0

UnitCost($/piece)

E


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400 #N/A #N/A #N/A $4.52 $4.65425 #N/A #N/A #N/A #N/A $4.61450 #N/A #N/A #N/A #N/A $4.57

Cost Breakdown @ 50,000

Unit Costs

Material $3.48Other Var $0.50

Equip $0.90Tooling $0.00

Other Fixed $0.56

Total Cos $5.44

0%

25%

50%

75%

100%

Fra

ction

ofTotalCost

Cost Breakdown By Ele


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alysis atory

Unit Cost Pizza Thic$5.44 6

Past 10 $2.33Mass 13 $2.58

16 $2.90

19 $3.28

22 $3.73

25 $4.2528 $4.83

31 $5.48

34 $6.19

37 $6.97

40 $7.82

6

10 $2.3313 $2.58

16 $2.90

19 $3.2822 $3.73

25 $4.25

28 $4 83

20 40 60

Production Volume (thousands)

fect of Production Volume

Var. Cost

Total Cost


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$5.44 Old New1 77.23468 1 28.39702 77.23468

5 18 62633 5 8 858801 18 62633

0 200 400 600

Production Volume (parts/year)

ent

Other Fixed

Tooling

Equip

Other Var

Material


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160 #N/A 160 4.585136 #N/A

170 #N/A 170 4.549225 #N/A

180 #N/A 180 4.517303 #N/A

190 #N/A 190 4.488742 #N/A200 #N/A 200 4.585131 #N/A210 #N/A 210 4.55606 #N/A220 #N/A 220 4.529632 #N/A230 #N/A 230 4.505502 #N/A240 #N/A 240 4.585128 #N/A250 #N/A 250 4.560708 #N/A260 #N/A 260 4.538167 #N/A

270 #N/A 270 4.517296 #N/A


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ness

6.5 7 7.5 8 8.5 9 9.5 10 10.5

$2.33 $2.34 $2.34 $2.35 2.352296 2.357415 2.362533 2.367651 2.37277$2.59 $2.60 $2.61 $2.61 2.622571 2.631221 2.639871 2.648521 2.657171$2.91 $2.92 $2.94 $2.95 2.963352 2.976455 2.989558 3.002661 3.015764

$3.30 $3.32 $3.34 $3.36 3.374639 3.393116 3.411594 3.430071 3.448548

$3.76 $3.78 $3.81 $3.83 3.856433 3.881206 3.905979 3.930752 3.955524

$4.28 $4.31 $4.34 $4.38 4.408733 4.440723 4.472713 4.504702 4.536692

$4.87 $4.91 $4.95 $4.99 5.03154 5.071668 5.111796 5.151924 5.192051

$5.53 $5.58 $5.63 $5.68 5.724853 5.77404 5.823228 5.872415 5.921602

$6.25 $6.31 $6.37 $6.43 6.488672 6.547841 6.607009 6.666177 6.725345

$7.04 $7.11 $7.18 $7.25 7.322998 7.393069 7.463139 7.533209 7.603279

$7.90 $7.98 $8.06 $8.15 8.227831 8.309724 8.391618 8.473512 8.555405

6.5 7 7.5 8 8.5 9 9.5 10 10.5

$2.33 $2.34 $2.34 $2.35 2.352296 2.357415 2.362533 2.367651 2.37277$2.59 $2.60 $2.61 $2.61 2.622571 2.631221 2.639871 2.648521 2.657171

$2.91 $2.92 $2.94 $2.95 2.963352 2.976455 2.989558 3.002661 3.015764

$3.30 $3.32 $3.34 $3.36 3.374639 3.393116 3.411594 3.430071 3.448548$3.76 $3.78 $3.81 $3.83 3.856433 3.881206 3.905979 3.930752 3.955524

$4.28 $4.31 $4.34 $4.38 4.408733 4.440723 4.472713 4.504702 4.536692

$4 87 $4 91 $4 95 $4 99 5 03154 5 071668 5 111796 5 151924 5 192051


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Working Areax 1 mm

Dough Temp 20 C

11 Oven Temp 225 C

2.3778882.665821 Target Temp 60 C3.028867

3.467025 thickness 5 mm

3.980297 alpha

4.568682

5.232179 potato = 1050 kg/m3

1050

5.97079 cp,potato = 3.64 kJ/kgK 3.64

6.784513 kpotato = 0.55 W/mK 0.55

7.67335 potato = 1.510-7

m2/s 7.50E-09

8.637299 h = 400 W/m2K

11

2.377888 202.665821 60 20.58817

3.028867 120 27.17807

3.467025 180 37.46433.980297 240 47.88762

4.568682 300 57.39662

5 232179 360 65 82632


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1440 131.27451500 132.95191560 134.5429

1620 136.05461680 137.4933

1740 138.86471800 140.1738


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t 9 sec

erf 1.00

Temp (x,t) 20 C

Target Temp @ 300 sec

20 2 4 6 8 10

60 113.4916 47.88762 25.1962 20.58817 20.03976

120 142.6231 79.82736 43.3385 27.17807 21.72364

180 156.7257 99.83186 60.32467 37.4643 26.44199

240 165.4246 113.4916 74.0283 47.88762 32.79352

300 171.4709 123.5219 85.04872 57.39662 39.59405

360 175.9859 131.2745 94.06864 65.82632 46.27005420 179.5227 137.4933 101.5951 73.25831 52.58606480 182.3902 142.6231 107.985 79.82736 58.46464

540 184.7759 146.9476 113.4916 85.66485 63.89885

600 186.8011 150.6571 118.2975 90.88461 68.91157660 188.5483 153.8845 122.5378 95.5811 73.53672

720 190.0758 156.7257 126.314 99.83186 77.81084

780 191.4261 159.2519 129.7044 103.7004 81.76912840 192.631 161.5173 132.77 107.239 85.44391

900 193.7149 163.5638 135.5591 110.4908 88.86438

960 194 6967 165 4246 138 1108 113 4916 92 056310

10

20

30

40

50

60

70

80

90

100


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2 4 6 8 1060 113.4916 47.88762 25.1962 20.58817 20.03976

120 142.6231 79.82736 43.3385 27.17807 21.72364180 156.7257 99.83186 60.32467 37.4643 26.44199

240 165.4246 113.4916 74.0283 47.88762 32.79352300 171.4709 123.5219 85.04872 57.39662 39.59405360 175.9859 131.2745 94.06864 65.82632 46.27005

420 179.5227 137.4933 101.5951 73.25831 52.58606480 182.3902 142.6231 107.985 79.82736 58.46464540 184.7759 146.9476 113.4916 85.66485 63.89885600 186.8011 150.6571 118.2975 90.88461 68.91157

660 188.5483 153.8845 122.5378 95.5811 73.53672720 190.0758 156.7257 126.314 99.83186 77.81084

780 191.4261 159.2519 129.7044 103.7004 81.76912

840 192.631 161.5173 132.77 107.239 85.44391

900 193.7149 163.5638 135.5591 110.4908 88.86438960 194.6967 165.4246 138.1108 113.4916 92.05631

1020 195.5915 167.126 140.4567 116.2716 95.04244

1080 196.4115 168.6896 142.6231 118.8561 97.842811140 197.1665 170.133 144.6316 121.2668 100.4751200 197.8646 171.4709 146.5004 123.5219 102.95461260 198.5128 172.7156 148.245 125.6375 105.29531320 199.1166 173.8773 149.8785 127.627 107.50921380 199.6809 174.9649 151.4121 129.5026 109.607

1440 200.2099 175.9859 152.8558 131.2745 111.5983

1500 200.707 176.9469 154.2178 132.9519 113.49161560 201.1753 177.8535 155.5056 134.5429 115.29451620 201.6176 178.7107 156.7257 136.0546 117.014

1680 202 0362 179 5227 157 8838 137 4933 118 656


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6

8

10


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10

13

16

19

22

25

28

31

34

37

40

6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11

Pizza Diameter

Pizza Thickness

Impact of Design Changes ($/pizza)

$8.00-$10.00$6.00-$8.00

mit msl pizzamodel (1)

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