assembly systems and assembly line balancing

Dr. Tafesse Gebresenbet

AAU, Technology Faculty

Mechanical Engineering Department

Email [email protected]

MEng 6106- Manufacturing Systems Modeling & Performance Analysis

Lecture II - Assembly Systems and Line Balancing

References : Mikel Groover, Automation, production systems and CIMAskin, Standridge, Modelling and analysis of Manufacturing systems

Manufacturing systems modeling & perofrmance analysis (TGS)

Assembly Systems and Line Balancing

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Assembly involves the joining together of two or more separate parts to form a new entity, called a subassembly, an assembly or some similar name.

Three major categories of processes used to accomplish the assembly of the components:

1. Mechanical fastening2. Joining methods3. Adhesive bounding



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1. Mechanical fastening: A mechanical action to hold the components together. Includes:

Threaded fasteners: Screw, nuts, bolts, etc. Very common in industry. Allow to be taken apart if necessary.

Rivets, crimping, and other methods: he fastener or one of the components is mechanically deformed.

Press fits: The two parts are joined together by pressing one into the other. Once fitted, the parts are not easily separated.

Snap fits: One or both of the parts elastically deform when pressed together. Commercial hardware such as retainers, C-rings, and snap rings may be used.

Sewing and stitching: Used to assemble soft, thin materials such as fabrics, cloth, leather, etc.



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2. Joining methods: Includes welding, brazing, and soldering. Molten metal is used to join two or more components together. Common feature of welding techniques is that fusing and melting occur in the metal parts being joined.In brazing and soldering, only the filler metal becomes molten for joining. The metal components do not melt. Not as strong as welding.

3. Adhesive bonding: Involves the use of an adhesive material to join components. Two types of adhesives: thermoplastic and thermosetting. Thermosetting adhesives are more complicated to apply, but are stronger and capable of withstanding in high temperature.


Assembly systems

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The methods used to accomplish assembly processes:1. Manual single-station assembly: Generally used on a

product that is complex and produced in small quantities. One or more workers are required depending on the size of the product. Ex: machine tools, industrial equipment, aircraft, ships, etc.

2. Manual assembly line: Consist of multiple workstations. One or more workers perform a portion of the total assembly work on the product.

3. Automated assembly system: Uses automated methods at the workstations rather than human beings.

Manual Assembly Lines Used in high-production situations where the work can be

divided into small tasks (work elements) and the tasks assigned to the workstations on the line.

By giving each worker a limited set of tasks repeatedly, the worker becomes a specialist in those tasks and perform more quickly. (Division of labor)


Assembly systems

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Transfer of Work Between Workstations1. Non mechanical Lines: Parts are passed from station to station

by hand. Problems are:Starving at stationsBlocking of stations

As a result, cycle times vary. Buffer stocks are used to overcome.2. Moving Conveyor Lines: Use a moving conveyor (ex. A moving

belt, conveyor, etc.) to move the subassemblies between workstations. The system can be continuous, intermittent (synchronous), or asynchronous.Problems of continuously moving conveyor:

StarvingProducing incomplete items

In the moving conveyor line, production rate may be controlled by means ofq feed rate. = feed rate = conveyor speed (feet per minute or meters per second) = spacing between parts

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Assembly systems

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Raw work parts are launched onto the line at regular intervals.

The operator has a certain time period during which he/she must begin work before the part flows past the station. This time period is called the tolerance time. = tolerance time = length of the station

Model VariationsIt is highly desirable to assign appropriate amount of work to the stations to equalize the process or assembly times at the workstations. This brings the line balancing problem and the three different types of lines.

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Assembly systems

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1. Single Model Line: Specialized line dedicated to the production of a single product.

2. Batch-model Line (Multiple parallel lines): Used for the production of two or more models with similar sequence of processing or assembly operations.

3. Mixed-model Line: Several models are intermixed on the line and are processed simultaneously.

These cases may be applied to both manual flow lines and automated flow lines.Type 2 and 3 are easier to apply to manual flow-lines.The problem of line balancing becomes more complicated when going from type 1 to type 3.


Multiple parallel lines

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ADVANTAGES easy work load balancing increasing scheduling

flexibility job enrichment higher line availability more accountability

DISSADVANTAGES higher setup costs higher equipment costs higher skill requirements slower learning complex supervision

As with most problems, multiple objectives exist. By far the most commonly used objective for analytical models is minimization of idle time.

However, in practice, real world issues of minimizing tooling investment, minimizing the maximum lift or strain by any worker, grouping tasks requiring similar skills, minimizing movement of existing equipment, and meeting production targets cannot be overlooked.


Workstation cycle time

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PACED LINESEach work station is given exactly the same amount of time to

operate on each unit of product. At the conclusion of this cycle time TC, the handling system automatically indexes each unit to the next station

ROLE OF BUFFERSUsually small buffers may be needed in non-automatic assembly to

avoid starving. Without buffers if task times vary, un paced (asynchronous) lines may be preferable.

UNPACED LINES (ASYNCHRONOUS)The station removes a new unit from the handling system as soon

as it has completed the previous unit, performs the required tasks, and then forwards the unit on to the next station.

PARALLEL WORKSTATIONS IN SERIAL SYSTEMS In many serial systems, each station along the line is usually a set

of parallel identical workstations. Each workstation in a parallel set performs similar activities.


The Line Balancing Problems

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It is to arrange the individual processing and assembly tasks at the workstations so that the total time required at each station is approximately the same.

Very difficult to achieve perfect balance in most practical situations.

If workstation times are unequal, the slowest station determines the overall production rate of the line.

TERMINOLOGY

Minimum Rational Work Element. The smallest practical indivisible tasks into which the job can be divided.

= Time required to carry out this rational work element.

Considered to be constant. In fact it varies in a manual station.

Assumed that they are additive. In fact it changes when two are combined at one station

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Total Work Content. ( ) Sum of the time of all the work elements to be done on the line.

= Number of work elements that make up the total

work or job.

Workstation Process Time. ( ) The sum of the times of the work elements done at the station.

n= number of stations

Cycle Time. ( ) Ideal or theoretical cycle time of the flow line. The time interval between parts coming off the line.

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Balance Delay. (balancing loss) (d) Measure of the line inefficiency.

The balance delay d will be zero for any values n and that satisfies the relationship

Minimum number of workstations required to optimize the balance delay for a specified may be found by

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Line Balancing

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The Basic objective of Line Balancing problemTo assign work elements to workstations such that assembly cost is minimized

Total assembly cost includes:Labor cost (while performing tasks)Idle time costFocus: minimize idle timeLimits: production constraints


Line Balancing

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Problem formulationproduction rate P (units/time)number of parallel lines mnumber of tasks N time to perform task i : ti

total task time T = ∑i=1N ti

to meet demand: cycle time Tc =m/p no worker must be assigned a set of tasks of duration longer than

m/p =Tc

Some Features of the Task order partially determinedassembly order constraints IP =(u,v) (i.e. task u must precede task

v)

zoning restrictions task pairs to same station ZS task pairs not performed in same workstation ZD


Line Balancing

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Objective function featureslowered number stations fill up firstonly stations with at least one task are constructedbenchmarking gage: proportion of idle timeidle time = (paid -productive)

BALANCE DELAY(measures proportion of idle time)

D = (K* Tc - ti)/(K* Tc)

= idle time/paid time

where K* is the number of stations required by the solution


Line Balancing

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Decision variables task i assigned to station k ? total number of tasks N

Cost coefficient Cik

NCik≤ Ci, K+1, k =1,2,3, …., K-1

K is the number of maximum workstations allowed. This allows forcing tasks onto the lowest numbered stations so that unused stations may be discarded.

Xik = {1,0} , 1- if task is assigned to station k; 0- otherwise

total number of stations k

Problem Formulation Minimize (Cik Xik) Subject to:

ti Xik < Tc (all stations k) [the sum of the tasks assigned doesn’t exceed cycle time}

Xik = 1 (all tasks i) [the task is assigned to exactly one workstation]

Xvh < Xuj (all k) & (u,v) in IP [ adherence to the precedence restriction]

(Xuk Xvk)=1 (all k) & (u,v) in ZS

Xuh+Xvh < 1 (all k) & (u,v) in ZD


Line Balancing

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CommentsD is idle time over paid timeobjective does not allocate idle time equally

among stnsbest solutions: good work load balancingtotal task time T = ti

Maximum time per station is Tc

minimum stations (lower bound) Ko = | T/TC |


LINE BALANCING APPROACHES

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Largest Candidate ruleKilbridge and Wester’s methodRPWHCOMSOALOPTIMAL SOLUTIONS

TREE GENERATION & EXPLORATIONPROBLEM STRUCTURE RULESFATHOMING RULES


Line Balancing

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They are heuristic approaches - based on logic and common sense rather than on mathematical proof. They do not guarantee an optimal solution, but result in good solutions which approach the true optimum.

1. Largest-candidate rule:

PROCEDURE

Step 1: List all elements in descending order of .

Step 2: Start from the top and select an element that satisfies the precedence requirements and does not cause the sum of the values at the station to exceed the cycle time .

Step 3: Continue to apply Step 2 until no further elements can be added without exceeding .

Step 4: Repeat steps 2 and 3 for the other stations until all the elements have been assigned.

The practical realities of the line balancing problem may not permit the realization of the most desirable number of stations.

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2. Kilbridge and Wester’s method:

PROCEDURE

Step 1: Construct the precedence diagram so that the nodes with identical precedence are arranged vertically in columns.

Step 2: List the elements in order of their columns. If an element can be located in more than one column, list all the columns by the element to show the transferability of the element.

Step 3: To assign elements to workstations, start with the column I elements. Continue to the assignment procedure in order of column number until the cycle time is reached. Go on until all elements are allocated.

In general, this method provides a superior line balancing solution when compared with the largest-candidate rule.


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3. Ranked positional weights method: Ranked Positional Weight HeuristicA single sequence is constructedA task is prioritized by cumulative assembly time associated with

itself and its successorsTasks are then assigned to the lowest numbered feasible

workstationPROCEDURE

Step 1: Calculate the ranked positional weight value (RPW) for each element by summing the element’s Te together with the Te values for all the elements that follow it in the arrow chain of the precedence diagram.Step 2: List the elements in descending order of their RPW. Step 3: Assign elements to stations according to RPW, avoiding precedence constraint and time-cycle violations.

S(i) successor tasks to task iPW(i) = ti + tj ; j in S(i)


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Ranked positional weights method

Let tasks be ordered, then Let PW(i) be the positional weight of taks i and let S(i) be the set of its successors. Thus

PW(i) = ti + ∑ tj ; j in S(i)

Task r Є S(i) if and only if there is a path of immediate successor relations from i to r.

Let the Immediate Successors be IS(i) and the Immediate Predecessors be IP(i)

The RPWH procedure as follows

1. Task ordering: For all i=1,2, …. N compute PW(i) and order the tasks by increasing values of PW (i)

2. Task assignment: For ranked tasks i, assign them in sequence to the first feasible station


COMSOAL

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4. COMSOAL - A Computerized Line Balancing MethodPROCEDURE : Computer Method for Sequencing Operations for Assembly

LinesSimple record keeping to allow examination of many possible

sequencesSequences are generated by random picking a task and

constructing subsequent tasksNew stations are opened when neededSequences that exceed the best solution are discardedBetter sequences become upper bounds

Step 1: Construct list A, showing all work elements in one column and the total number of elements that immediately precede each element in an adjacent column.Step 2: Construct list B, showing all elements from list A that have no immediate predecessors.


COMSOAL (for generation X trial)

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Array of Number of Immediate Predecessors for each task i NIP(i) Array of for which other tasks is i an immediate predecessor WIP(i) Array of N tasks TK, c- available time remaining in current workstation List of unassigned tasks A List of tasks from A with all immediate predecessors assigned B List of tasks from B with tasks times not exceeding remaining cycle time in

the current workstation F

1.- SET

x=0, UB=∞, cycle time, c=Tc

2.- Start new sequence: SET x=x+1, A=TK, NIPW(i) = NIP(i)

3.- Precedence feasibilityFOR all i Є A, IF NIPW(i) = 0 , ADD i TO B

4. Time feasibilityFOR i Є B, IF ti < c ADD i TO F . If F empty , 5 , otherwise 6

5.- Open new stationIDLE=IDLE + c , c = TC

If IDLE > UB , 2, otherwise 3


COMSOAL (contd’)

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6.- Select task: SET m = card{F}Random generate RN Є U(0,1)LET i* = [m*RN] th TASK from FRemove i* from A,B,Fc = c - tiFOR ALL i Є WIP(i*), NIPW=NIPW-1IF A EMPTY Go to 7, OTHERWISE Go to 3

7.- Schedule completionIDLE = IDLE + cIF IDLE < UB , UB = IDLE Go to STORE SCHEDULEIF x = X , STOP, OTHERWISE Go to 2


Optimization of Line Balancing

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Consider the construction of a decision tree with all possible sequences obeying precedence constraints. The tree starts at the root and evolves to the first branches; the tasks without predecessors.

Form there, the next level of possible task evolve. The process continues until we reach the leaves. The path from the root to each leaf constitutes a complete sequence. The optimal sequence is the one of the leaves but which one? Optimization procedures are based on searching decision trees for the optimal leaf.



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Depth first Backtracking

In the depth first backtracking we first generate the tree. Then we start with a leaf and backtrack towards the root of the tree.

Assume the number of decision to be made is N. The choices available at stage n depend on earlier decisions.

The tree is generated considering only the ordering of the tasks. At any stage, eligible tasks are those whose predecessors have already been included in the partially completed sequence. Sequences thus created necessarily satisfy precedence constraints.

One proceeds depth first by growing the tree by selecting first alternative at each stage until a terminal leaf is reached. Next we backtrack from the leaf towards the root until unexplored branch is reached. Then we move again depth first generating a different sequence. Next we backtrack again and repeat until all possible leaves are explored.



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To solve the problem, a sequence is selected and divided into workstations fulfilling the cycle time constraint and starting new stations only when absolutely necessary. This requires the concept of fittable task, i.e., a task if fittable into a station if

it fits into the remaining idle time of the station It is still unassigned, and All its predecessors have been assigned

The procedure is then as follows:1. Input bound and task data 2. Setup; k=1; p=0; Ck=Tc; B=0

3. Select new task: Find i’= lowest i; i fittabel i>N. Does i’ exists?. If yes got to 6; otherwise go to 3.

4. Assign task: Ai=k; p=p+1; Ck = Ck-ti*; B=0. Is p=N? If yes got to 6; otherwise go to 3.

5. Open new station: k=k+1; Ck=TC

6. Sequence complete; Save it if best solution7. Backtrack to B (remove B from station K) If Ck=Tc, k=K-1,

B=Tap; AB=0; Ck-Ck+tB; p=P-1; i*= go to 3.



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The problem can be simplified by “pruning” the tree i.e., only creating those new nodes required for the search of a better solution.

Fathoming rules are introduced such that if a node satisfies one of the rules all paths from that node can be discarded. This process is called fathoming the node. Once all remaining nodes are either fathomed or are leaves we are alone.

The following optimality principles need always be invoked. Never close a station while fittabel tasks remain If a task makes all others unfittabel, make it a work station.

The list of fathoming rules is as follows Task dominance Station dominance Solution dominance Bound violation Excessive idle time

Mixed Model lines

The objective function is the same to spread the work load among stations as evenly as possible can be expressed as follows. In mixed assembly model assembly line balancing, total work element times per shift or per hour are used. and Minimize (wAT-WL) or minimize

Where w-number of workers or stations ( we are assuming the Mi =1, so that n=w, w=WL/ATWL-work load to be accomplished by the workers in the scheduled time period (min/hr)AT =available time in the period of interest (min/hr/worker)TTs= total service time at station i to perform its assigned portion of the work

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Work load can be calculated

The total time to perform each element in the work load is calculated

Where TTk – the total time within the workload that must be allocated to element k for all products (min)

Total service times at each stations are computed

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Measures of balance efficiency for mixed assembly line balancing corresponds to those in single model line balancing:

Where Eb- balance efficiency

WL-work loadw – number of workers(stations) max{TTsi}- maximum value of total service

time among all stations in the solution

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SEQUENCING MIXED MODELS

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We assume qj – the proportion of the product type j, j=1,….P to be producedThe first step is to develop an assembly line balance for the weighted average product.

Let tij be the time to perform the task i on product type j and

sk the set of tasks assigned to the workstation k

We can state an average feasibility condition ∑iЄSk ∑j=1 p

qj tij ≤ Tc k=1,….K

In solving this problem we use ti =∑j=1 p qj tij

1.- Initialization: create list of all products to be assigned (A)

2.- Assign a product (List A)FOR n from list A, create list B of all product types assignable

without violating constraints from list B select product which minimizes the function

| ∑j=1 n ∑iЄSkb ti,j(n) - n Ckb |Add product type j* to the nth positionRemove a product type j* from A IF n < NGO TO 1


SEQUENCING MIXED MODELS

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Subject to the following constraints

∑j=1 N = Nj j=1,…., p

(to ensure that all items are produced during the cycle)

nNj – s1 ≤ ∑j=1 n Xjb ≤ nNj/N + s1 n=1,…., N j= 1, ….P

(to restrict the production rate of each product to be within s1 of its average rate at all times)

∑b=1 n ∑j=1

P ∑iЄsk tiXjb ≤ (n+s2)Ck n= 1,….N k=1,….K

(limit the maximum overutilization at all times)

Xjn = 0 or 1

The constraints attempt to restrict unplanned station idle time due to strarving. While the formulation appears complex, use of a greedy approach to the objective yields a straightforward sequencing heuristic.


UNPACED LINES

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Paced line with K stations and cycle time TC, theEach time spends KTC in system (throughput

time)Production rate is 1/ TC

In a deterministic unpaced lineProduction rate is 1/ TC

Time in system is maybe not KTC

WIP is smaller for unpaced lines


Other Ways to Improve the Line Balance

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Dividing work elementsChanging work head speeds at automatic stationsMethods analysisPreassembly of componentsInventory buffers between stationsParallel stations

assembly systems and assembly line balancing

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