A New COMSOAL Based Heuristic Approach to...
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A New COMSOAL Based Heuristic
Approach to Mixed Model
Assembly Line Balancing with
Parallel Workstations and Zoning
Constraints
Ramazan YAMAN and Ibrahim KUCUKKOCBalikesir University, Department of Industrial Engineering, Cagis Campus, Balikesir / Turkey
[email protected], [email protected]
YAEM/2011, Sakarya
Introduction
• This paper presents a new approach for the mixed model assembly line balancing problem, which includes some issues that reflect the operating conditions of real world assembly lines such as parallel workstations and zoning constraints. A new COMSOAL (Arcus, 1965) based heuristic procedure has been developed and its performance has been evaluated by an illustrative example and standard test cases from literature.
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Classification
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Classification of ALB Models
based on Problem Structure
According to ALB
Model Type
Single Model ALB
(smALB)
Mixed Model ALB
(mALB)
Multi Model ALB
(muALB)
According to ALB
Problem Structure
Simple ALB
(sALB)
General ALB
(gALB)
Figure 1: Classification of Assembly Line Balancing Models
•smALB: only one product is produced,
•mALB : similar products or variations of different models of a product are
produced simultaneously and continuously (not in batches),
•muALB: more than one product produced in batches.
Classification
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The illustration of sMALB, mALB and muALB can be seen in Figure 2. In the
muALB, setup or preparation time is required between the different models.
Mixed-Model Assembly Line
Single-Model Assembly Line
Multi-Model Assembly Line
S S
Assembly Lines According to Model Types
Figure 2: Assembly line types
Set up
Model 1
Model 2
Model 3
S
Literature ReviewPublications Line Configuration Methodology Test Problem
Askin and Zhou (1997) Straight line, parallel st. Nonlinear integer programming, heuristic Randomly generated
McMullen and Frazier (1997) Straight line, parallel st. Heuristic, simulation Randomly generated
Gokcen and Erel (1997) Straight line Binary goal programming More than one
Gokcen and Erel (1998) Straight line Binary integer programming More than one
Erel and Gokcen (1999) Straight line Network programming Only one problem
Merengo et al. (1999) Paced and unpaced
linesHeuristic Randomly generated
Kim, Kim, and Kim (2000) Straight line Co-evolutionary based heuristic Benchmark problems
Vilarinho and Simaria (2002) Straight line, parallel st. Mathematical model, simulated annealing Randomly generated
Bukchin et al. (2002) Straight line Mathematical model, heuristic Only one problem
McMullen and Tarasewich
(2003) Straight line, parallel st. Ant colony optimization, simulation Benchmark problems
Zhao et al. (2004) Paced line Heuristic Randomly generated
Hop (2006) Straight lineFuzzy binary linear programming,
heuristicRandomly generated
Bock (2006) Straight line Distributed search procedures More than one
Bukchin and Rabinowitch
(2006) Straight line
Branch and bound algorithm based
heuristicRandomly generated
Noorul Haqetal.(2006) Straight line Hybrid genetic algorithm More than one
Kara et al. (2007) U-line Simulated annealing Randomly generated
Bock (2008) Straight line Tabu search Randomly generated
Simaria and Vilarinho (2009) Two-sided line Ant colony optimization Benchmark problems
Ozcan and Toklu (2009) Two-sided line Mathematical model, simulated annealing Benchmark problems
Akpinar and Bayhan (2011) Straight line Hybrid genetic algorithm Benchmark problems
Yagmahan (2011) Straight line Multi-objective ant colony optimization Benchmark problems
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mALB Types
• According to the objective functions, there are three types of mALB in the literature (Scholl, 1995):
▫ mALB-I: The number of workstations is to be minimized for a given cycle time (i.e., production rate).
▫ mALB-II: The cycle time is to be minimized for a given number of workstations.
▫ mALB-E: The cycle time and the number of workstations are to be minimized at the same time.
• All of the versions of the problem are NP-Hard. This study deals with mALB-I.
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Mathematical Model
• In the model, the fitness function that proposed by (Leu, Matheson, & Rees, 1994) was used as objective function (see Equation 1). Thus, workload smoothing between the workstations was considered as an additional goal to minimization of workstations and total idle times.
where C, Wk and S denote the cycle time of the assembly line, work load of the station and the number of workstations required to meet the demand in the assembly line, respectively.
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The mCOMSOAL Procedure
• COMSOAL (Computer Method of Sequencing Operations for Assembly Lines) was developed around 1965 by Arcus. COMSOAL produce several possible assembly line balances by considering the constraints.
• The simple COMSOAL method used to solve the mALB problem has the following comparatively basic procedure (Wild, 1989):
1. Construct List A showing all unassigned works and the total number of elements which precede them in the precedence diagram.
2. Construct List B showing all elements which have no predecessors (i.e. elements with a zero predecessor value of List A).
3. Select at random one element From List B, and assign it to solution sequencing.
4. Eliminate the selected element from the precedence matrix and List A.
5. If there is an unassigned element, go to Step1, otherwise go to Step 6.
6. Tag the solution as a feasible individual.
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The mCOMSOAL Procedure
• Proposed mCOMSOAL method also uses this procedure in the problem solving process. But the main differences between the COMSOAL and proposed mCOMSOAL method are objective function and constraints to reflect the realistic conditions in real world assembly lines. The mCOMSOAL method allows parallel workstations to perform the tasks that exceed the cycle time (if any of the task time larger than the workstation capacity). Besides, the mCOMSOAL method has positive and negative zoning constraints that mean some of the tasks must be performed in the same workstation or otherwise.
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Create a feasible initial solution
with COMSOAL
START
Assign works to workstations
(allow parallelization if one or
more tasks exceed capacity)
Compute the fitness value of
the solution
Tag the solution as
feasible and qualifiedExceed
maxiter?
Rank the solutions according to
their fitness values
STOP
Yes
No
No
Yes
Choose the solution which has the
best fitness value as the best
solution of the problem
Keeps the
zoning
contraints?
Figure : Flow chart of COMSOAL based new heuristic procedure
An Illustrative Example
• In this section a numerical example is given to illustrate the proposed mCOMSOAL method. The precedence diagram has been taken from Kilbridge and Wester (School, 1993), and task times from Simaria (2006).▫ In the example, two models are simultaneously assembled in the
same assembly line and over a planning horizon of 480 time units.
▫ The demand for each model (A and B) is 20 and 28 units, respectively. Thus, the cycle time (C) is equal to 480/(20+28)=10. The weighted average task times computed by the production sharing of the models (q1 =20/(20+28)=0.42; q2=28/(20+28)=0.58) are given in Table 2.
▫ The combined precedence diagram with 45 tasks is depicted in Figure 5.
▫ A workstation can be replicated if it performs a task with a processing time larger than the cycle time.
▫ Task 18 and task 19 cannot be executed on the same workstation and similarly, tasks 23 and 32.
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An Illustrative Example-Task Times
Task 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1,0 4,4 14,3 2,2 4,8 5,1 0,0 5,1 9,4 5,0 3,5 0,0 7,0 2,7 5,3
1,0 5,1 0,0 2,2 4,8 5,8 10,0 5,1 9,4 5,0 3,5 4,0 0,0 0,0 5,3
Weighted Average
Task Time1,0 4,8 6,0 2,2 4,8 5,5 5,8 5,1 9,4 5,0 3,5 2,3 2,9 1,1 5,3
Task 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0,0 2,2 0,0 8,3 2,6 2,5 5,7 9,7 3,7 9,6 8,8 4,8 8,0 5,6 4,0
3,0 2,2 3,0 8,3 2,6 2,5 5,7 8,8 3,7 9,6 8,8 4,8 0,0 5,6 4,0
Weighted Average
Task Time1,8 2,2 1,8 8,3 2,6 2,5 5,7 9,2 3,7 9,6 8,8 4,8 3,3 5,6 4,0
Task 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
4,8 8,6 10,0 5,4 4,7 9,4 1,0 7,3 4,1 1,2 1,1 2,4 1,7 12,3 2,5
4,4 8,6 8,9 5,4 5,4 9,4 1,0 6,9 4,1 1,4 1,0 2,4 1,7 13,5 2,5
Weighted Average
Task Time4,6 8,6 9,4 5,4 5,1 9,4 1,0 7,1 4,1 1,3 1,0 2,4 1,7 13,0 2,5
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Table 2: Processing times and average task times for the numerical example (Simaria, 2006)
An Illustrative Example-Sample Solution
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5 2 8 3 1 . . 17 29 42 37 43 27 5,168
Task 1 Task 45
Total Station Number
Fitness Value
WS 1 WS 2 … WS 27
Figure 4: Representation of a sample solution
An Illustrative Example-Precedence Relationships
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10
29
30
31
32
25
17
16
18
23
24
9
6
14
15
5
43
4
8
13
7
3
37
2
11
112
26
27
19 20 21 22
34
36
35
33
28
38
40
39 41 42 44
45
An Illustrative Example-Best Solution
S Tasks R Workload S Tasks R Workload
1 11, 12 1 5,8 13 22, 14, 17 1 9,0
2 2, 13, 37 1 8,7 14 31, 27 1 9,4
3 8, 39 1 9,2 15 32 1 8,6
4 4, 15, 43 1 9,2 16 25 1 9,6
5 23 1 9,2 17 26 1 8,8
6 6, 24 1 9,2 18 28, 29 1 8,9
7 16, 18, 10 1 8,6 19 33 1 9,4
8 19, 1 1 9,3 20 36 1 9,4
9 3 1 6,0 21 30, 34 1 9,4
10 5, 20 1 7,4 22 35 1 5,1
11 7, 21 1 8,3 23 38, 40, 41 1 9,4
12 9 1 9,4 24 42,45,44 2 17,9
S=25, Minfit=3,45 Meanfit=5,19 Maxfit=6,73
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Table 3: Illustration of the best solution
Benchmark Problems
# Problem Description N M C LBpmixAkpinar&
Bayhan
mCOMSOAL Fitness Value
RunTime
(Sec.)Min S' D(%) Min Mean Max
1 Vilarinho and Simaria 25 2 10 14 16 14 0,00 2,19 2,82 4,35 10 36,01
2 Vilarinho and Simaria 25 3 10 14 14 14 0,00 2,34 3,15 4,31 10 31,62
3 Heskiaoff 28 2 10 19 20 20 0,05 1,85 3,05 9,74 10 52,45
4 Heskiaoff 28 3 10 18 20 19 0,06 2,54 3,31 4,03 10 67,41
5 Sawyer 30 2 10 15 16 16 0,07 2,40 3,01 4,49 10 65,43
6 Sawyer 30 3 10 17 19 19 0,12 4,43 5,19 5,35 10 74,70
7 Lutz1 32 2 10 16 19 17 0,06 3,20 3,62 4,90 10 84,34
8 Lutz1 32 3 10 17 19 18 0,06 3,83 4,62 5,05 10 101,66
9 Tonge 70 2 10 41 44 46 0,12 5,65 6,46 6,96 10 122,02
10 Tonge 70 3 10 39 44 45 0,15 3,84 5,47 6,09 10 114,72
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Table 4: Computational results for the chosen test problems
Conclusion
• In this study, it is discussed that mixed model assembly line balancing with parallel workstations and zoning constraints. A new COMSOAL based algorithm was developed to solve the complex problem efficiently. Objective function (Leu et al., 1994) and constraints (Vilarinho and Simaria, 2002) used in the mathematical model derived from the previous studies in the literature.
• For the problems 1, 4, 7 and 8 the mCOMSOAL produces better solutions than hybrid GA (Akpinar and Bayhan, 2011), however for the problems 9 and 10 hybrid GA produces more suitable solutions compared to mCOMSOAL. For the problems 2, 3, 5 and 6 the situation is in tie.
• The results show that it is simply possible to solve all of the small, medium and large sized mixed model assembly line balancing problems with parallel workstations and zoning constraints using mCOMSOAL procedure. Both of the mALB-1 and mALB-2 problems should be discussed together in the future researches.
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