Int J Adv Manuf Technol (2006) 28: 337–341 DOI 10.1007/s00170-004-2373-3

ORIGINAL ARTICLE

A. Noorul Haq · J. Jayaprakash · K. Rengarajan

A hybrid genetic algorithm approach to mixed-model assembly line balancing

Received: 4 May 2004 / Accepted: 9 August 2004 / Published online: 20 April 2005 © Springer-Verlag London Limited 2005 Abstract Assembly line balancing has been a focus of interest to academics in operation management for the last four decades. Mass production has saved huge costs for manufacturers in various industries for some time. With the growing trend of greater product variability and shorter life cycles, traditional mass production is being replaced in assembly lines. The current market is intensely competitive and consumer-centric. Mixed-model assembly lines are increasing in many industrial environments. This study deals with mixed-model assembly line balancing for n models, and uses a classical genetic algorithm approach to minimize the number of workstations. We also incorporated a hybrid genetic algorithm approach that used the solution from the modified ranked positional method for the initial solution to reduce the search space within the global space, thereby reducing search time. Several examples illustrate the approach. The software used for programming is C++ language. Keywords Genetic algorithm · Hybrid algorithm · Mixedmodel assembly line balancing

1 Introduction An assembly line is a set of sequential workstations linked by a material handling system. In each workstation, a set of tasks are performed using a predefined assembly process in which the following issues are defined: (a) task time, the time required to perform each task; and (b) a set of precedence relationships, which determines the sequence of the tasks. The A. Noorul Haq (u) · K. Rengarajan Department of Production Engineering, National Institute of Technology, Tiruchirapalli-620 015, India E-mail: [email protected] J. Jayaprakash Department of Mechanical Engineering, Pachari Sri Nallathankal Amman (PSNA) College of Engineering and Technology, Dindigul-624 622, India

current market is intensely competitive and consumer-centric. For example, in the automobile industry, most of the models have a number of features, and the customer can choose a model based on their desires and financial capability Different features mean that different, additional parts must be added on the basic model. Due to high cost to build and maintain an assembly line, the manufacturers produce one model with different features or several models on a single assembly line. Under these circumstances, the mixed-model assembly line balancing problem arises to smooth the production and decrease the cost. Since the demands for different models and for features vary on a daily basis, the problem should be solved everyday in industry. Formally, a mixed-model assembly line balancing problem can be stated as follows: given n models, the set of tasks associated with each model, the performance times of the tasks, and the set of precedence relations which specify the permissible orderings of the tasks for each model, the problem is to assign the tasks to an ordered sequence of stations such that precedence relations of each model are satisfied and some performance measures are optimized. Unlike the case of a single model line, different models of a product are assembled on a mixed-model assembly line. The models are launched to the line one after another. Two types of assembly line balancing problems are: 1. Type-I problems, where the required production rate (i.e. cycle time), assembly tasks, tasks times, and precedence requirements will be given and the objective is to minimize the number of workstations; and 2. Type-II problems, where the number of workstations or production employees is fixed and the objective is to minimize the cycle time and maximize the production rate. These types of balancing problems are generally occur when the organization wants to produce the optimum number of items using a fixed number of workstations without purchasing new machines or expanding its facilities. This study is mainly focused on the Type-I problem, which aims to minimize the number of workstations.

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2 Literature review The mixed-model with deterministic assembly line balancing model is very applicable in “just in time” manufacturing environments because attempts have been made to find sequences resulting in minimal WIP levels. Helgeson and Birnie [1] solved the assembly line balancing problem using a ranked positional weight technique. Kabir and Tabucanon [2] solved the batchmodel assembly line (two or more products) problem using a multi-attribute-based approach. Monden [3] was concerned with the sequencing of assembly lines such that the stability of parts usage rates would be addressed. Miltenburg [4] presented a heuristic approach to both measure the stability of parts usage rates and to minimize the “lumpiness” of raw material usage. Erel and Gokcen [5] used shortest-route formulation to minimize the task time for different models while also considering precedence constraints. Erel and Gokcen [6] developed a binary integer formulation for the mixed-model assembly line balancing problem. In another work, Erel and Gocken developed a goal programming approach [7] in which they used a combined precedence diagram, which had been previously developed by Thomopoulos [8]. A two-stage heuristic method for balancing mixed-model assembly lines was developed by Vilarinho and Simaria [9]. The application of genetic algorithms (GA) for assembly line balancing has been widely studied so for. Anderson and Ferris [10] proposed a genetic algorithm for Type-II problems, and Leu, Matheson and Rees [11] presented a GA-based approach to solve Type-I problems with multiple objectives. A genetic algorithm for work load smoothing was presented by Kim, Kim and Kim [12]. Chen, Lu and Yu [13] developed a hybrid genetic algorithm approach to the assembly line planning problem. All these studies are different from this work not only in terms of the problem considered, but also in terms of the hybrid approach. This study presents a hybrid GA approach to solve the mixed model assembly line balancing problem. Initially, a wellknown heuristic method is used to generate a feasible solution. This solution is then included into the randomly-derived population of an evolving pool of GA. The goal of including a heuristics solution in this population is to reduce the search space from the size of the global space, thereby reducing the search time.

3. No WIP inventory buffer is allowed between stations. 4. Parallel stations are not allowed. 5. Common tasks exist between models, which must be assigned to the same stations. The concept of a combined precedence diagram is to transform different models into an equivalent single model. The combined diagram is constructed by taking the union of the nodes and the precedence relations of the diagrams of all the models. The construction of the combined diagram is straightforward with precedence matrices. A simple example is given in Fig. 1 to illustrate the process of constructing a combined diagram. The

3 Model description The mixed-model assembly line balancing approach utilizes the concept of combined precedence diagrams to join the precedence relations of different models in a single diagram. Typically, there are several tasks common to the various models manufactured on a mixed model assembly line, with similar precedence relations among these tasks. Thus, the similarity between the precedence relations of different models has been utilized. The assumptions of the model are listed below: 1. Task time of each models are known constants. 2. Precedence diagram for each models are known.

Fig. 1a–c. Precedence diagrams of a model A b model B c combined precedence diagram

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numbers within the circles represent tasks, and the arrows connecting the circles specify the precedence relations. The objective function of the problem is Min

k


Ak

k=1

where k = Number of stations, Ak = Total number of stations. = 1 if station k is utilized by any one model.

cycle time. Now, we multiply the respective task times of the models by corresponding production shares and add up the task time for all the models to get average task time. Next, we determine the positional weight (PW) for each task using the average task time. The positional weight of a task in a mixed-model assembly line is the cumulative average task time associated with itself and its successors. Then we rank the work elements based on the PW and proceed to assign work elements to the workstations, where elements of the highest PW and rank are assigned first. If at any workstation additional time remains after the assignment of an operation, we assign the next succeeding ranked operation to the workstation, as long as the operation does not violate the precedence relationships and cycle time.

4 Hybrid Approach

4.3 Hybrid genetic algorithm

Gentic algorithm have been proven effective in many combinatorial optimization problems, and it seems natural to apply the approach to a mixed-model assembly line balancing. To improve the capability of searching for a good solution, we introduce a hybrid genetic algorithm with the modified ranked positional weight method (MRPW). First, a classical GA method is used to test the problem and then solved by the modified ranked positional weight method. Finally, the solution generated by the heuristic method is introduced randomly into initial pools and proceed by the GA method.

In the proposed hybrid genetic algorithm, the initial solution is obtained from the modified ranked positional weight method and included in the initial population of the genetic algorithm. This approach reduces the search space from the size of the global space, thereby reducing the search time.

4.1 Genetic Algorithm Genetic algorithms are stochastic search methods that mimic the metaphor of natural biological evolution. Genetic algorithms operate on a population of potential solutions applying the principle of “survival of the fittest” to produce increasingly better approximations to a solution. At each generation, a new set of approximations is created by the process of selecting individuals according to their level of fitness in the problem domain, and breeding them together using operators borrowed from natural genetics. This process leads to the evolution of better suited populations. The three most important aspects of using genetic algorithms are: 1. definition of the objective function; 2. definition and implementation of the genetic representation; and 3. definition and implementation of the genetic operators. At the beginning of the computation a number of individuals (the population) are randomly initialised. 4.2 Modified ranked positional weight method (MRPW) The modified ranked positional weight method was introduced by Helgeson and Birnie [1] for a Type-I single model line balancing problem. Here, we apply this method in mixed model balancing. First, we determine the number of models and the production share of each model, and then we calculate the production share of each model in terms of the percentage having a fixed

5 Experiments and analysis We applied two similar models to a mixed-model assembly line balancing problem. The precedence diagrams of the two models and their tasks times are given in Table 1. Note that as shown in Fig. 1, the combined diagram has 11 tasks, where as the first and second models have seven and nine tasks, respectively. Cycle time is 10 min for each model. 5.1 Genetic algorithm The experiment is first solved by genetic algorithm for various models. The inputs for the genetic algorithm procedure such as population size, crossover probability, mutation probability is 50, 0.8 and 0.05. Also, the task time of the models and precedence

Table 1. Task time for two models No of tasks 1 Models

2

3

4

5

6

7

8

9

10

11

Model A Model B

5 –

4 4

– 1

– 5

– 6

2 2

4 –

3 3

– 5

3 3

1 1

Table 2. Optimal station assignment of the illustrative example: GA No of Task at Model A Station time Model B Station time work station each station (s) (s) 1. 2. 3.

1,4,5,8,9 3,6,2 10,7,11

1,8,9 3,2 7,11

8 9 5

1,4,5,9 3,6 10,7,11

10 10 10

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diagrams of the two models are given as input. The optimal station assignment of the illustrative example for classical GA is given in Table 2. The execution time for this example is 391 s.

Table 5. Comparison of GA and MRPW No of observation

No of models taken

Total task in combined diagram

Number of workstations MRPW Genetic algorithm

1 2 3 4 5 6 7

2 3 4 5 6 7 8

9 12 13 15 16 16 18

5 6 8 6 8 13 13

5.2 Modified ranked positional weight method The demand for each of the models are equal and the weighted task times are given for calculating the positional weights. The positional weights and the ranking of the tasks for the illustrative example are given in Table 3. The optimal station assignment of the illustrative example for the modified ranked positional weight method is given in Table 4. A comparison of the results for various models is given in Table 5. It reveals that the classical GA method offers superior solutions, compared to the modified ranked position weight method. The graphical representation of the results is shown in Fig. 2.

3 4 5 4 5 8 10

Table 6. Comparison of pure GA and hybrid GA No of observation

No of models taken

Total no of tasks in combined diagram

Processing time (s) Classical GA Hybrid GA

1 2 3 4 5 6 7

2 3 4 5 6 7 8

9 12 13 15 16 16 18

136 553 226 324 631 718 832

5.3 Hybrid genetic algorithm The experiment is also tested by a hybrid genetic algorithm for various models. The inputs for the hybrid genetic algorithm procedure such as population size, crossover probability, mutation

86 200 116 214 376 595 627

Table 3. Positional weight of the tasks No of tasks 1

2

3

4

5

6

7

8

9

10

11

5 — 2.5 7.5 8

4 4 4 9 5

— 1 0.5 11 2

— 5 2.5 10.5 3

— 6 3 8 7

2 2 2 5 10

4 — 2 10.5 4

3 3 3 8.5 6

— 5 2.5 5.5 9

3 3 3 3 11

Models Model A Model B Average task time Positional weight Rank

1 1 1 12 1

Table 4. Optimal station assignment of the illustrative example: MRPW Work stations

Task at each station

Station time (s)

1 2 3 4 5

1,4,5 8,3 9,6 2,10 7,11

7 8 9 10 5

Fig. 3. Comparison of GA and hybrid GA

probability are 50, 0.8 and 0.05. Also, the task time of the models and precedence diagrams of the two models are given as input. The solutions from the MRPW are randomly inserted into the initial pools and retested. The execution time of the hybrid genetic algorithm is found to be less than that of the classical GA. The execution time for this illustrative example is 110 s. A comparison of the results for the various models is given in Table 6. It reveals that the hybrid GA method is superior to the classical GA in terms of execution time. The graphical representation of the results is shown in Fig. 3.

6 Conclusion Fig. 2. Comparison of GA and MRPW

In this study, we have presented a hybrid genetic algorithm approach to solve the mixed-model assembly line balancing prob-

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lem. The genetic algorithm approach is shown to produce better results than the modified rank position weight in the minimization of workstations. Next, we combined the solution of the MRPW approach with that produced by a genetic algorithm and make a hybrid genetic algorithm. This approach results in better performance than a classical genetic algorithm.

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5. Erel E, Gokcen H (1999) Shortest-route formulation of mixed-model assembly line balancing problem. Eu J Oper Res 116:194–204 6. Erel E, Gokcen H (1998) Binary integer formulation for mixed-model assembly line balancing problem. Comput Ind Eng 23:451–461 7. Erel E, Gokcen H (1997) A goal programming approach to mixedmodel assembly line balancing problem. Int J Prod Econ 48:177–185 8. Thomopoulos NT (1967) Line balancing-sequencing for mixed model assembly. Manage Sci 4(2):B59–B75 9. Vilarinho PM, Simaria AS (2002) A two-stage heuristic method for balancing mixed-model assembly lines with parallel workstations. Int J Prod Res 40:405–1420 10. Anderson EJ, Ferris MC (1994) Genetic algorithms for combinatorial optimization: Assembly line balancing problem. ORSA J Comput 6:161–173 11. Leu YY, Matheson LA, Rees LP (1994) Assembly line balancing using genetic algorithm with heuristic-generated initial population and multible evalution criteria. Dec Sci 25:581–606 12. Kim YK, Kim YJ, Kim Y (1996) Genetic algorithms for assembly line balancing with various objectives. Comput Ind Eng 30:397–409 13. Ruey-Shun C, Kun-yung L, Shien-chang Y (2002) A hybrid genetic algorithm approach on assembly line planning problem. Eng Appl Artif Intell 15:447–457