A New COMSOAL Based Heuristic Approach to Mixed Model Assembly Line Balancing with Parallel Workstations and Zoning Constraints Ramazan YAMAN and Ibrahim.

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]/2011, Sakarya

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06.07.2011 Yaman and Kucukkoc YAEM/2011, Sakarya

Toyota Car Manufacturing Factory

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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.


4

Classification


Classification of ALB Models based on Problem Structure

According to ALBModel Type

Single Model ALB(smALB)

Mixed Model ALB(mALB)

Multi Model ALB(muALB)

According to ALBProblem 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.

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Classification


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

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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 lines

Heuristic 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, heuristic

Randomly generated

Bock (2006) Straight line Distributed search procedures More than one

Bukchin and Rabinowitch (2006)

Straight lineBranch and bound algorithm based heuristic

Randomly 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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Mathematical Model


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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.06.07.2011 Yaman and Kucukkoc YAEM/2011, Sakarya

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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 qualified

Exceed 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

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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 Time

1,0 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


1,8 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


4,6 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


Table 2: Processing times and average task times for the numerical example (Simaria, 2006)

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An Illustrative Example-Sample Solution


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

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An Illustrative Example-Precedence Relationships


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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

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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


Table 3: Illustration of the best solution

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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


Table 4: Computational results for the chosen test problems

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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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References• Akpinar, S., & Bayhan, G. (2011). A hybrid genetic algorithm for mixed model assembly line

balancing problem with parallel workstations and zoning constraints. Engineering Applications of Artificial Intelligence , 449-457.

• Askin, R. G., & Zhou, M. (1997). A parallel station heuristic for the mixed-model production line balancing problem. International Journal of Production Research , 3095 - 3106.

• Baybars, İ. (1986). A Survey of Exact Algorithms for the Simple Assembly Line Balancing Problem. Management Science , 909-932.

• Boysen, N., Fliedner, M., & Scholl, A. (2007). A classification of assembly line balancing problems. European Journal of Operational Research , 674–693.

• Bukchin, J., Dar-el, E. M., & Rubinovitz, J. (2002). Mixed model assembly line balancing in a make-to-order environment. Computers&Industrial Engineering , 405-421.

• Bukchin, Y., & Rabinowitch, I. (2006). A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs. European Journal of Operational Research , 492-508.

• Chong, K. E., Omar, M. K., & Bakar, N. A. (2008). Solving Assembly Line Balancing Problem using Genetic Algorithm with Heuristics-Treated Initial Population. Proceedings of the World Congress on Engineering 2008. London: WCE 2008.

• Gen, M., Cheng, R., & Lin, L. (2008). Network Models and Optimization, Multiobjective Genetic Algorithm Approach. London: Springer.

• Gokcen, H., & Erel, E. (1997). A goal programming approach to mixed-model assembly line balancing problem. International Journaal of Production Economics , 175-185.


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References

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• Scholl, A. (1993). Data of Assembly Line Balancing Problems.• Scholl, A. (1995). Balancing and sequencing of assembly lines. Darmstadt: Physica-Verlag .• Scholl, A. (1996). Simple Assembly Line Balancing-Heuristic Approaches. Journal of Heuristics ,

217-244.• Simaria, A. S. (2006). Assembly line balancing - new perspectives and procedures. PhD Thesis.

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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.

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