A New COMSOAL Based Heuristic
Approach to Mixed Model
Assembly Line Balancing with
Parallel Workstations and Zoning
Constraints
Ramazan YAMAN and Ibrahim KUCUKKOC
Balikesir University, Department of Industrial Engineering,
Cagis Campus, Balikesir / Turkey
[email protected], [email protected]
YAEM/2011, Sakarya
2
Toyota Car Manufacturing Factory
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
3
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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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Classification
Classification of ALB Models
based on Problem Structure
According to ALB
Model Type
According to ALB
Problem Structure
Single Model ALB
(smALB)
Simple ALB
(sALB)
Mixed Model ALB
(mALB)
General ALB
(gALB)
Multi Model ALB
(muALB)
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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YAEM/2011, Sakarya
06.07.2011
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Classification
Assembly Lines According to Model Types
Single-Model Assembly Line
Model 1
Model 2
Model 3
Mixed-Model Assembly Line
S Set up
Multi-Model Assembly Line
S
S
Figure 2: Assembly line types
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.
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YAEM/2011, Sakarya
06.07.2011
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Literature Review
Publications
Line Configuration
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)
Network programming
Only one problem
Heuristic
Randomly generated
Kim, Kim, and Kim (2000)
Straight line
Paced and unpaced
lines
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)
McMullen and Tarasewich
(2003)
Zhao et al. (2004)
Straight line
Hop (2006)
Straight line
Bock (2006)
Bukchin and Rabinowitch
(2006)
Noorul Haqetal.(2006)
Straight line
Merengo et al. (1999)
Methodology
Mathematical model, heuristic
Test Problem
Only one problem
Straight line, parallel st. Ant colony optimization, simulation
Benchmark problems
Paced line
Randomly generated
Straight line
Heuristic
Fuzzy binary linear programming,
heuristic
Distributed search procedures
Branch and bound algorithm based
heuristic
Hybrid genetic algorithm
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
Yaman and Kucukkoc
Straight line
YAEM/2011, Sakarya
Randomly generated
More than one
Randomly generated
More than one
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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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YAEM/2011, Sakarya
06.07.2011
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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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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Mathematical Model
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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START
Create a feasible initial solution
with COMSOAL
Assign works to workstations
(allow parallelization if one or
more tasks exceed capacity)
No
No
Compute the fitness value of
the solution
Keeps the
zoning
contraints?
Yes
Exceed
maxiter?
Tag the solution as
feasible and qualified
Yes
Rank the solutions according to
their fitness values
Choose the solution which has the
best fitness value as the best
solution of the problem
STOP
Figure : Flow chart of COMSOAL based new heuristic procedure
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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An Illustrative Example-Task Times
Table 2: Processing times and average task times for the numerical example (Simaria, 2006)
Task
1
2
3
4
5
6
1,0 4,4 14,3 2,2 4,8 5,1
7
0,0
8
9
10
11
12
13
14
15
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
1,0 4,8
Task Time
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
17
18
19
21
22
23
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
1,8 2,2
Task Time
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
33
34
36
37
38
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
4,6 8,6
Task Time
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
Task
Task
Yaman and Kucukkoc
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31
32
20
35
YAEM/2011, Sakarya
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39
25
40
26
41
27
42
43
06.07.2011
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An Illustrative Example-Sample Solution
WS 1
5
2
WS 2
8
3
1
.
Total Station
Number
…
WS 27
.
17 29 42 37 43 27
5,168
Fitness Value
Task 1
Task 45
Figure 4: Representation of a sample solution
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YAEM/2011, Sakarya
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An Illustrative Example-Precedence Relationships
6
10
29
2
4
30
8
31
32
14
11
13
15
7
12
1
25
26
17
27
16
19
18
28
20
21
33
34
23
36
35
3
5
24
37
43
9
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22
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42
44
45
38
40
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An Illustrative Example-Best Solution
Table 3: Illustration of the 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
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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Benchmark Problems
Table 4: Computational results for the chosen test problems
mCOMSOAL
Fitness Value
#
Problem Description N
M
C
LBpmix
Akpinar&
Bayhan
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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06.07.2011
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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.
Yaman and Kucukkoc
YAEM/2011, Sakarya
06.07.2011
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References
•
•
•
•
•
•
•
•
•
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YAEM/2011, Sakarya
06.07.2011
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