Assembly Line Balancing in an Automotive Cables Manufacturer Using a Genetic Algorithm Approach

Hager Triki, Ahmed Mellouli, Wafik Hachicha, Faouzi Masmoudi Laboratory of Mechanic, Modeling and Production (L2MP) Engineering School of Sfax, Tunisia

hager_triki@yahoo.fr

Abstract—In general, assembly lines, allow low production costs, reduced cycle times and accurate quality levels. Assembly line balancing problem (ALBP) is about how to group the assembly activities, which have to be performed in an assembly task, into workstations, so that the total assembly time required at each workstation is approximately the same (cycle time). In this paper, an ALBP is studied in a real-world automotive cables manufacturer company. This company found it necessary to balance its line, since it needs to increase the production rate. In this line type, the number of stations is known and the objective is to minimize cycle time where both precedence and zoning constrains must be satisfied. For this purpose, a hybrid genetic algorithm (HGA) based on genetic algorithm scheme and local search procedures is implemented and fully characterized. The results of comparative studies with CPLEX software exact solutions show that the proposed HGA approach is very effective and competitive

Keywords—Assembly line balancing problem; precedence and zoning constrains; cycle time; hybrid genetic algorithm approach; real-world case study

I. INTRODUCTION An assembly line balancing problem (ALBP) consists of

distributing the total workload for manufacturing products among the stations along the manufacturing line. Research has focused on developing effective and fast solution methods for solving the simple assembly line balancing problem (SALBP) [1] and their various extensions. Each extension is motivated by several real-life applications and the need for solving precise practical problems. In this paper, we study the process of assembly line balancing of motor cables in the multinational company LEONI (http://www.leoni.com) to increase the production rate. The company is a global supplier of wires, optical fibbers, cables and cable systems as well as related development services for many applications in industries especially the automotive business. In this industry, we describe a balancing assembly line when zoning constrains exist among some pairs of tasks. For example, some raw materials (file, tube etc...) can be so similar to each other that quality consideration and the processing conditions force certain pairs of tasks to be assigned to different stations.

The main characteristics of this ALB Problem (ALBP) are as follows: (a) the performance time of each operation is deterministic (b) the precedence relationship among assembly tasks is known and invariable (c) a simple product type is

assembled on the line (d) no buffer is considered between the stations (e) The zoning constraints are included in tasks assignment to stations. In this situation, the number of stations is known and the objective is to minimize cycle time where both precedence and zoning constrains must be satisfied. All these constraints make this ALBP very hard to solve.

In literature, there are various applications of metaheuristics to solve large scale of ALBPs. Among these metaheuristics, Genetic Algorithms (GAs), which is received an increasing attention from the researchers since it provides an alternative to traditional optimization techniques by using directed random searches to locate optimum solutions in complex landscapes [2]. GAs are a stochastic procedure which imitates the biological evolutionary process of genetic inheritance and the survival of the fittest. As a population-based approach, GA has two main advantages:

• GA can find a population of solutions rather than a single solution in a single run. Consequently, the likelihood that the algorithm will be trapped in a local optimum decreases.

• GA fitness function can take any form and several fitness functions can be used simultaneously [2]

Therefore, we chose to apply the GA method because it is a powerful tool used to found good solutions for NP hard problems

Although there are plenty of previous researches that use the algorithms, only the underlying and the related GA framework adopted in this paper is presented due to space limitation. Those readers who are further interested in GA may refer to [3] and [4].

The majority of these previous studies have validated their GA performances using simulate problem, but little via real case studies data. For example, [5] developed a GA to solve SMALB Type-1 problem in the clothing industry in order to maximize the line efficiency. Reference [6] reduced the cycle time by 28.5% of a real two sided car assembly line by applying a GA. However, these studies have not integrated an optimization tool to choose their AG parameters. Since the problem is NP-hard, a hybrid genetic algorithm (HGA) based on genetic algorithm scheme and local search procedures is implemented and fully characterized. The main steps of HGA are explained in the next section.

International Conference on Advanced Logistics and Transport

978-1-4799-4839-0/14/$31.00 ©2014 IEEE 336

The outline of the rest of this paper is as follows: Section 2 presents the steps of the proposed HGA. Section 3 illustrates the experimental results to select HGA parameters. Section 4 shows computational results. Finally, concluding remarks are presented in Section 5.

II. STEPS OF HYBRID GENETIC ALGORITHM The flow chart of the proposed HGA is presented in Fig. 1.

The initialisation of the HGA contains the creation of the initial population (the first generation of the genetic process). Besides, a local search and crossover and mutation operators are used to improve the quality of solutions.

Fig. 1. Flowchart of the proposed HGA

A. Coding and Initial Population(Phases 1 and 2) The encoding scheme is task-oriented and it is similar to

the scheme generated by [7]. The length of the chromosome is equal to the number of tasks and each gene of the chromosome defines a task. The initial population is randomly generated, assuring the feasibility of the precedence relations.

B. Fitness Evaluation (Phase3) In general, GA aims at finding the most fitted chromosome

over a set of generations. The fitness function provides a measure of an individual’s performance (fitness) in the search space. The proposed HGA employs the fitness of a chromosome (individual) as the inverse of the cycle time of the solution to be suitable with a minimisation problem. Therefore, the lowest cycle time the solution has, the more important its fitness is.

f(j)= C1

(1)

f(j): denote the fitness function value of chromosome j; j = 1, . . .,J. The fitness value evaluates individual performance in the search space. Fig. 2. Precedence graph G of the illustrative example

The cycle time of the chromosome is determined by the following steps: Step1: Determine the initial cycle time value which is Lower Bound (LB) calculated as follow:

LB=max ( { }ni

it≤≤1

max ,m

tn

ii∑

=1 ) (2)

Step2: Determine the number of stations by the following procedure [8]: Tasks are assigned to stations according to the task sequence in the chromosome as long as the predetermined cycle time is not overtaken. Once this cycle time is surpassed at least for a model, or the zoning constraints of set IT ,which presents the set of incompatible pair tasks, are not satisfied, a new station is opened for assignment and the procedure is repeated until the last task is assigned [8]. Step 3: If the obtained number of station is equal to a given m go to Step 4, else the cycle time C will be incremented by 1 and go to Step 2. Step4: Terminate the procedure and present the cycle time of chromosome. To present all phases of the proposed approach (in Fig. 3), an illustrative example will be explained. The Fig. 2 presents the precedence graph G. m=6 stations (S), n=10 tasks, the tasks 4 and 5 are incompatible Step1 C=LB=8

Step3 C=LB=8 m =7>6 C=C+1= 9 go to step2

Step3 C=9 m =6 The desired number of stations Step4 End procedure: The cycle time of this chromosome is C=9

Fig. 3. The assignment of tasks to stations of the illustrative example

C. Stopping Criteria (Phase4) The HGA procedure will stop when one of the following

conditions is achieved.

Chromosome associated to G 1 2 3 4 5 6 8 7 9 10

Step2 Task time 8 8 4 2 2 6 8 2 5 2 Station S1 S2 S3 S4 S5 S6 S7

Step2 Task time 8 8 4 2 2 6 8 2 5 2 Station S1 S2 S3 S4 S5 S6

Best Solution

Yes

Phase 2: Random generation of initial population (All Individuals are feasible)

Phase 3: Evaluation of each individual (Fitness Evaluation)

Phase 5: Recombination: Selection (Roulette Wheel) and Crossover (Four Points)

Phase 6: Mutation

Phase 7: Evaluation of all offsprings (Fitness Evaluation)

Phase 9: Updating a new generation with the best chromosomes

Phase 4: Stopping Criteria satisfied

No

Phase 8: Application of a local search for every offspring (Task Sequence Search) and evaluation of new offsprings

Phase 1: Chromosome Encoding

106

3

2

51

48

9

8

2

4

2 6

8

2

5

2

8

7

337

1) The fitness function of the best solution does not improve more than 1% after a predetermined number of consecutive iterations (this value is set to 50 by default).

2) The total number of iterations exceeds a maximum number (1000 is the value set by default). It should be noted that these default values of parameters are illustrated and selected according a set of randomly generated instances through a simple convergence study.

D. Selection and Crossover Operator (Phase 5) Each individual in the population parent is selected by the

‘‘Roulette Wheel Strategy" [9]. 1) First Crossover Operator (Two crossover points)

The First Crossover Operator (FCO) was introduced by [10]. It works as follows:

• Two points randomly selected, cut the parent into three parts (0-1, 1-2, 2-3).

• All elements from the parts (0-1, 2-3) of the first parent are copied to identical positions in the offspring1.

• All the elements within the part (1-2) of the first parent are reordered according to the order of their appearance in the second parent vector to generate the remaining parts of offspring1.

The other offspring is generated using the same method, with the roles of its parents reversed.

2) Second Crossover Operator (Four crossover points) The Second Crossover Operator (SCO) uses four crossover points as indicated Fig. 4, it works as follows:

• four points generated randomly, cut each parent into five parts (0-1, 1-2, 2-3, 3-4, 4-5), as shown in the Fig. 3.

• All elements from parts (0-1, 2-3, 4-5) of the first parent are copied to identical positions in the offspring 1.

• All the elements within the parts (1-2, 3-4) of the first parent are reordered according to the order of their appearance in the second parent vector to generate the remaining parts of offspring 1.

The second offspring is generated by the same steps, with the roles of its parents reversed.

Fig. 4. Second Crossover Operator (SCO)

E. Mutation Operator (Phase 6) The procedure consists in randomly choosing two

positions within the solution offspring as it is shown in Fig. 5. These two positions cut the offspring into three parts (fragments). We put fragement1, fragement2 and fragement3 which are presented as follows:

• Fragment 1: all elements are placed before the first position.

• Fragment 2: all elements are placed between the two positions.

• Fragment3: all elements are placed after the second position.

Fragment 1 and fragment 2 are projected on the new mutated offspring but fragment 2 undergoes a reconstruction procedure. This procedure which is adopted from [8] is carried out by removing all references to fragment1 in the prohibit table, and then randomly choosing a task among those in the table with no predecessor requirements. This new task is then added to the next locus in the chromosome and is removed from the prohibit table. The process continues until all tasks of fragment 2 are assigned. Fragment2 is reconstructed randomly in a manner that ensures feasibility. Fig. 5. Mutation operator

F. Evaluation of all Offsprings (Phase 7) The evaluation of each offspring is identical to the phase 3.

In every crossover and mutation, new candidate solutions are created. The new solutions may be better or worse. This means that performing solutions are to be replaced using a replacement strategy. Several strategies have been suggested in litetrature. These include the following: probabilistic replacement, crowding strategy, and elitist strategy. In this study, the elitist strategy has been adopted.

G. Local search procedure: Task Sequence Search (Phase8) Many researchers have used the local search procedure in

GAs for improving the convergence speed towards the global optimum and to reduce computation time ([10]; [11]). In this setting, a local search procedure (Task Sequence Search) is extended based on the concept of the bottleneck stations to obtain better task sequence so as to reduce the cycle time. The proposed local search is applied to every offspring before it is inserted into the population. Task sequence search is explained in four steps as follow: Step1: Identification of the bottleneck station b. Step2: Let i the first task of b. i has to be moved to another station q without violating the existing constraints (the precedence and zoning constraints). Step3: Let Tq the station time q. The move is worthwhile if Tq+ti <C, then q is worthwhile station and the procedure is stopped. Step4: If the worthwhile station does not exist for all possible stations in the line, i will be the next task in b (i=i+1). The procedure terminates with the last task. H. Updating a new population(Phase 9) The replacement strategy which is applied in [12] is used to create the new population. This strategy takes into account the

P1

P2

O1

O2

1 2 3 4 0 5

10 1 3 4 2 5 6 8 9 7

10 1 4 8 9 3 5 2 7 6

10 1 3 4 2 5 6 7 9 8

10 1 4 8 9 3 5 6 7 2

O

New O

1 3 4 5 6 2 8 7 9 10

1 3 4 5 2 6 7 8 9 10

338

fitness value of the individuals. The individuals of the new generation must have the best fitness (higher fitness value= minimum cycle time) of all individuals from:

1) The current population 2) Offsprings produced by crossover 3) Offsprings undergo mutation 4) Offsprings produced by local search 5) The current population

The best solution of each generation is stored to avoid its loss over the following generations.

III. HGA PARAMETERS SELECTION The proposed HGA implemented with MATLAB 7.6. All

experiments are run within Windows 7 Professional installed on a PC with Intel(R) Core (TM) i3-2310MCPU, 2.10 GHz. In order to characterize parameters and evaluate the performance of the HGA, a large set of problems should be tested. For this reason, the HGA parameters selection step is performed using 52 problems which their exact solution is known (Coptimal). The Coptimal is determined using the solver CPLEX 9.0 software as an interactive optimizer. The quality of the solutions obtained through the proposed HGA is evaluated through the percentage difference (E %) between the solutions presented according the proposed HGA (Cmin) and the Coptimal. E% is calculated as follows:

E% = optimal

optimal

C

CC )min(100 −× (3)

A. Stopping Criteria

The number of necessary iterations is not predefined. We have varied the stop number of iterations in order to minimise E% as indicated in table I.

TABLE I. EVALUATION OF THE E% FOR THREE NUMBERS OF ITERATIONS

Number of iterations

The maximum E% of all instances

The maximum compilation time (minutes)

10 20.23 0.83 100 15.33 6 500 12.56 15 1000 9.5 22 2000 9.5 50

Based on Table I, the number of iterations should be fixed at 1000 iterations. Indeed, it gives better E% (same value) with acceptable compilation time. In the next subsection, other HGA parameters will be selected using also the measure E%.

B. Selection of HGA parameter values The performances of HGA for both quality of solutions

and compilation time are related to the different HGA parameter values. Extensive testing and a setting of parameter values of the HGA are performed. The parameters that are assessed in this series of instances are:

• Population size (Pop size): The initial population size. • Crossover Operator (CO): We used two crossover

operator types. FCO is the most used in the literature;

however the SCO is newly performed in the balancing problems.

• Probability of mutation (Pmut): values between 0 and 1 indicate the probability that a newly generated solution string undergoes a single exchange of element positions.

A guided experimental study is necessary to perform the HGA parameters. For this reason, each parameter is divided into two levels. Pop size have two levels (50, 100), Crossover Operator (FCO, SCO), and Pmut (0.1, 0.15). It follows that 8 (23) experiments are necessary to select the better configuration, as mentioned in Table II.

TABLE II. HGA PARAMETERS VALUES TESTED

Configurations Pop size Crossover Operator Pmut C1 50 FCO 0.15 C2 50 FCO 0.10 C3 50 SCO 0.15 C4 50 SCO 0.10 C5 100 FCO 0.15 C6 100 FCO 0.10 C7 100 SCO 0.15 C8 100 SCO 0.10

To select the best parameters configuration, one-way Analysis of Variance (ANOVA) is applied using Minitab Software. To the right of the one-way ANOVA table, under the column headed P, is the P-value. In this case, P = 0.000. The P-value is for testing the hypothesis in above, the mean E% from the 8 configurations are the same vs. not all the means are the same. Because the P-value of 0.000 is less than specified significance level of 0.05, H0 is rejected. The data provide sufficient evidence to conclude that the mean E% from the eight configurations are not all the same. We can see below the ANOVA table, another table that provides the sample sizes (N = 52 problems), sample means, and sample standard deviations of the 8 samples. Beneath that table, the pooled StDev is given and this is an estimate for the common standard deviation of the 8 populations. Finally, the lower right side of the Minitab output gives individual 95% confidence intervals for the population means of the 8 experiments. Based on Fig. 6, the best configuration consists in selecting Pop size =100, crossover operator = SCO, and Pmut = 0.15.

One-way ANOVA: C1, C2, C3, C4, C5, C6, C7, C8

Source DF SS MS F P Factor 7 175.18 25.03 4.13 0.000 Error 408 2471.95 6.06 Total 415 2647.13

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev +------+-------+------+---- C1 52 3.406 2.850 (------*-----) C2 52 3.633 2.965 (-----*----) C3 52 2.387 2.197 (------*------) C4 52 2.604 2.326 (------*------) C5 52 2.840 2.613 (-----*------) C6 52 2.968 2.754 (------*-----) C7 52 1.677 1.787 (------*-----) C8 52 1.826 1.926 (-----*------)

339

+---------+---------+---------+--------- 1.0 2.0 3.0 4.0

Pooled StDev = 2.461

Fig. 6. One-way ANOVA results

IV. RESULTS OF HGA VALIDATION The proposed HGA was employed in many instances of assembly line motor cable. Table III shows the characteristics (task time and precedence relations) and the actual tasks assignment to stations of two test problems on assembly line of motor cables.

TABLE III. SET OF TEST PROBLEMS DATA

Instance number

The data The actual assignment

of tasks to stations

Predecessors Task Number

Task time (in s)

Station Station

time (in s)

Instance 1

4G197111C

m=3 n=14

0 1 5

1 69

0 2 6

1-2 3 40

0 4 8

4 5 10

0 6 5

2 63

6 7 9

7 8 19

8 9 10

3-5-9 10 20

10 11 8

3 57 11 12 9

11 13 28

12-13 14 12

Instance 2

713G-713J-713L

m=6 n=44

0 1 10

1 409

0 2 50

2 3 19

1-3 4 80

0 5 40

5 6 25

0 7 40

7 8 25

4-6-8 9 20

9 10 100

10 11 65

2 418 11 12 40

11 13 43

11 14 40

12-13-14 15 30

0 16 10

0 17 20

16-17 18 30

18-10 19 50

19 20 40

15-20 21 50

21 22 390

3 440 22 23 30

23 24 20

21 25 125

4 395

21 26 20

21 27 20

27 28 25

25-26-28 29 160

24-29 30 25

30 31 20

0 32 22

5 480

31 33 30

32-33 34 90

37-33 35 80

38-33 36 80

0 37 23

0 38 24

34-35-36 39 131

39 40 120

6 470

39 41 80

39 42 40

39 43 100

40-41-42-43 44 130

TABLE IV. SET OF VALIDATION TEST PROBLEMS

Instance Number

The obtained assignment of tasks to stations by CPLEX

optimisation software

The obtained assignment of tasks to stations by

proposed GA

Station (tasks)

Station time (in s)

Station (tasks)

Station time (in s)

1

1 (1,2,6,3,7) 65

1 (1,2,6, 3,7)

65

2 (8,9,4,5,10) 67

2 (8,9,4, 5,10)

67

3 (11,12,13,14) 57

3 (11,12, 13,14)

57

2 1

(1,2,3,4, 5,6,7,

432 1

(1,7,16,2,8, 5,6,32, 38,3,37

388

340

8,9,10,37)

4,9)

2 (11,12,13,14, 15,16,17,18, 19,20,21,27)

438

2 (17,18,10,

19,20,11,14, 12,13, 15)

458

3 (22,26,28) 435 3

(21,27,22) 460

4 (23,24,25,

29,30,31,33,38) 434

4 (25,26,23,

24,28,29,30, 31,33)

455

5 (32,34,35, 36,39,42)

443 5

(35,36,34, 39,42)

421

6 (40,41,43,44) 430

6 (43,40,41,

44) 430

Table IV contains the best solutions obtained by the CPLEX software and by the proposed HGA. As can be seen in table V, the cycle times found for these instances.

TABLE V. RESULTS OF SET OF VALIDATION TEST PROBLEMS

Problem n m Actual Cused of the line

Coptimal using CPLEX

Cobtained from the proposed HGA E%

1 14 3 69 67 67 0.00

2 44 6 480 443 460 3.83

Although the cycle time used in all instances is acceptable, the proposed HGA could make cycle time more efficient. We have determined the Coptimal by CPLEX optimisation software for these instances. The comparison between the results given by the HGA approach and the optimal cycle times shows an accomplishment of the proposed HGA. Moreover, the proposed HGA approach can make a significant improvement to performance of the company lines.

V. CONCLUSION In this real case, a new extension of SALBP is focus. In

this extension, the number of stations is known and the objective is to minimize cycle time where both precedence and zoning constraints must be satisfied. For this purpose, a hybrid genetic algorithm (HGA) based on genetic algorithm scheme and local search procedures is implemented and fully characterized. The results of comparative studies with CPLEX software exact solutions show that the proposed HGA approach is very effective and competitive. The performance

of the proposed HGA approach has been evaluated using E% metric which is a difference measure between exact solution using CPLEX software and obtained solutions using HGA approach. Discussions with industrial engineers and the results obtained in the practise case suggest some research topics perspectives:

1) Taking the resource assignment problem into account, the modelling might introduce the zoning constraints adapted to both tasks and resources. Moreover, many new criteria (price, speed of resource, and so on), which may not be optimised through this GA, have to be considered.

2) Adding other objectives to the problem such as initial and set up costs of resources.

REFERENCES

[1] I. Baybars, “ A survey of exact algorithms for the simple assembly line balancing problem ,” Manag. Sci., Vol. 21, 1986, pp. 909-932.

[2] S. O. Tasan and S. Tunali, “ A review of the current applications of genetic algorithms in assembly line balancing,” J. Intel. Manufactur., Vol. 19, 2008, pp.49–69.

[3] D. Eo. Goldberg, “Genetic Algorithms in Search,” Optimization and Machine Learning (Addison-Wesley, Reading, MA), 1989.

[4] G. E.Liepins , and M. R. Hilluard, “Genetic algorithms: foundations and applications,” Annals of Opera. Res., Vol. 21, 1989, pp. 31-58

[5] C. C. K. Chan, P. C. L. Hui, K.W. Yeung, and F. S. F. Ng., “Handling the assembly line balancing problem in the clothing industry using a genetic algorithm,” Int. J. of Clothing Science and Technol., Vol.10,1998, pp. 21–37.

[6] S. A. Valente, H. S. Lopes and L.V.R. Arruda, “Genetic algorithms for the assembly line balancing problem: A real-world automotive application,” In R. Roy, M. Köppen, S, 2002.

[7] I.Sabuncuoglu, E. Erel and M. Tanyer, “Assembly line balancing using genetic algorithms”. J of Intel. Manufact., Vol. 11, 2000, pp. 295–310.

[8] S. Akpına and G. MiracBayhan, “A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints,” Eng. Appl. of Artificial Intel. , Vol. 24, 2011, pp. 449–457.

[9] H.J. Holland “Adaptation in natural and artificial systems, ” Ann Arbor. Michigan: The University of Michigan Press, 1975.

[10] J. Rubinovitz and G. Levitin, “Genetic algorithm for assembly line balancing,” Int. J. Economics, Vol. 41, 1995, pp.343–354.

[11] J. Gao, L .Sun, L.Wang and M. Gen, “An efficient approach for type II robotic assembly line balancing problems,” Comput. and Indus. Engin., Vol.56, ,2009, pp. 1065–1080.

[12] A. S. Simaria and P.M. Vilarinho, “ A genetic algorithm based approach to the mixed-model assembly line balancing problem of type II,” Comput. & Industri. Engin. ,Vol. 47, 2004, pp.391–407.

341