Optimal Operator Assignment In An Assembly Line Using Genetic Algorithm

Optimal Operator Assignment in an Assembly Line using Genetic Algorithm 1 Optimal Operator Assignment In An Assembly Line Using Genetic Algorithm TANZINA ZAMAN, SANJOY KUMAR PAUL* AND ABDULLAHIL AZEEM Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh. Abstract: This paper addresses the operator assignment in predefined workstations in an assembly line to optimize cycle time, total idle time and output where genetic algorithm is used as an optimization tool. Operator assignment in an assembly line balancing is as important as job scheduling in workstations. To improve the efficiency and meet the desired target output within time limit, a balanced assembly line is a must. At real world lines are consisted of a large number of tasks and it is very time consuming and crucial to choose the most suitable operator for a particular workstation. Besides, it is very important to assign the suitable operator at the right place as his skill of operating machines finally reflects in productivity or in the cost of production. Moreover, the more the time a particular job is processed by a particular machine, the more the probability of being defective will be increased. So, to minimize that risk, it is desired to take less time to process a job, i.e. to minimize cycle time. To verify all the possible assignments of workers, genetic algorithm is adopted here. The purpose of this approach is to propose a heuristic to find out the optimal assignment of operators in the predefined workstations. Keywords: Operator assignment, Line balancing, Assembly line, Genetic algorithm. 1. INTRODUCTION Assembly Line Balancing (ALB) is one of the important problems of production/operations management area. As small improvements in the performance of the system can lead to significant monetary consequences, it is of utmost importance to develop practical solution procedures that yield high-quality design decisions with minimal computational requirements. Basically, Assembly Line Balancing Problems (ALBP) seek to assign a set of assembly tasks to an ordered sequence of workstations in such a way that precedence constraints are maintained and a given efficiency measure (e.g. number of workstations or the cycle time) is optimized. The worker assignment scheduling problem involves both the decisions of job scheduling and worker assignment. In the classic scheduling problem no matter how many machines (work stations, processors etc.) are involved, the number of operators (workers) at each machine may be ignored or assumed to be constant and is not taken into consideration. However, in some * Corresponding Author: sanjoy@ipe.buet.ac.bd cases, assigning more workers to work on the same job will decrease job completion time. Hence, ignoring worker assignment decision may cause managerial problems. In order to solve these problems and optimize the overall performance, decisions about job scheduling and operator assignment need to be resolved together. The mathematical formulation of the ALBP for simple assembly lines was first stated by Salveson (1955) and since then, extensive research has been done in the area. Numerous studies on ALBPs have been reported, including those by Rekiek et al. (2002), Becker and Scholl (2006) and Boysen et al. (2007). Despite the vast search space, many attempts have been made in the literature to solve the ALBP using optimum seeking methods, such as linear programming (Salveson, 1955), integer programming (Bowman, 1960) and dynamic programming (Held et al. 1963). However, none of these methods has proven to be of practical use for large problems due to their computational inefficiency. Hence, numerous research efforts have been directed towards the development of heuristics such Baybars LBHA (1986) and meta-heuristics such

2 Tanzina Zaman, Sanjoy Kumar Paul and Abdullahil Azeem as simulated annealing (Suresh and Sahu, 1994) and tabu search (Peterson, 1993) have been applied more recently. Genetic Algoritnm is a stochastic search method inspired by concepts from Darwinian evolution theory and belongs to a class of metaheuristic methods known as evolutionary algorithm (EA). As a solution approach, GA has two advantages: ( i) GA searches a population rather than a single point and this increases the likelihood that the algorithm will not be trapped in a local optimum since many solutions are considered concurrently, and (ii) GA fitness function may take any form and several fitness functions can be utilized simultaneously. Leu et al. (1994) developed a GA to solve SALB T ype-1 problems and used heuristic procedures to determine the initial population. Anderson and Fer ris (1994) presented a GA application to the SMALB Type-2 problem which shows the effective use of GAs solving combinatorial optimization problems. Rubinovitz and Levitin (1995) used a GA to obtain SALB Type-2 problem in, which the processing times of a task was dependent upon workstation assignment. Kim (1996) used a genetic algorithm to solve the assembly line balancing problem of how to minimize the number of workstations and cycle time, and how to maximize workload smoothness and work relatedness. Hence, job processing time is no longer a constant but related to the number of workers assigned to work on the job. Ponnambalam et al. (2000) in his paper, proposed a multi-objective genetic algorithm to solve assembly line balancing problems. The performance criteria considered are the number of workstations, the line efficiency, the smoothness index before trade and transfer, and the smoothness index after trade and transfer. The developed genetic algorithm is compared with six popular heuristic algorithms. Sabuncuoglu et al. (2000) proposed an efficient heuristic to solve the deterministic and single-model ALB problem. W.K. Wong (2005) adopted genetic algorithm proposed for optimizing the assignment of operators in an assembly line. The impact of a different level of skill inventory SIn on the assembly makespan is also investigated in order to find out the optimal number of task skills an operator should possess in the apparel assembly process. Boutevin (2006) proposed hybrid methods for line balancing problems. The objective of his study was to assign operations to workstations in order to minimize, for instance the number of required workstations. The basic constraints were cycle time and precedence constraints. In the research paper of Baykaso ğlu and Özbak ı r (2007), a new multiple-rule-based genetic algorithm (GA) is proposed for balancing U-type assembly lines with stochastic task times. Rajakumar et al. (2007) in his research used genetic algorithm (GA) to solve the parallel machine scheduling problem of the manufacturing system with the objective of workflow balancing. Kulak et al. (2008) proposed a GA-based solution approach for balancing printed circuit board assembly lines where a single type of PCB is assigned in highprecision placement machines to minimize the assembly cycle time. Guo et al. (2008) proposed a genetic-algorithm-based optimization model for scheduling flexible assembly lines where the objectives of minimizing the weighted sum of tardiness and earliness penalties and balancing the production flow of the FAL. Tseng et al. (2008) worked with integrated sequence planning problem, which is solved using a genetic algorithm approach with an objective of lowest operation costs. The above works are mainly focused on job assignment in workstations and optimizing number of workstations, cycle time, workload smoothness and work relatedness. The effect of machine dependency of operators is not focused in any of the above studies. This paper focuses on finding an approach for optimum operator assignment in Simple Assembly Line Balancing (SALB) Type-2 not being limited to any specific assembly process. As many attempts have been taken to assign jobs in workstations, only operator assignment is considered here assuming that jobs are already assigned to workstations. 2. PROBLEM DEFINITION In assembly line, there are a number of tasks and a number of machines in which the tasks are processed. Each task may not be processed in each machine. For balancing assembly line, tasks are assigned to a set of workstations where tasks are processed in a pre-defined sequence. While assigning operator in workstations, it is assumed that every operator is equally skilled in operating each machine. But in practical cases operating skill may vary depending on type of machines. A typical scenario of assembly line is shown in Fig. 1. There are M numbers of workstations and N types of machines are required to get the complete product. Every station may not have all the types of

Optimal Operator Assignment in an Assembly Line using Genetic Algorithm 3 machines. Only one operator is assigned in each station. Efficiency level of operators varies from r 1 to r 2, considering average task time as the base. Skill combinations of h types to operate N types of machines can be represented by skill matrix of h N. Effective working hour in a day is dependent upon efficiency factor, E which ranges from E 1 to E 2. The problem is to assign operators in workstations in such a way that cycle time, C and total idle time, I is minimized and daily production rate, P is increased compared to theoretical cycle time, Cth; total idle time, Ith and daily production rate, Pth. The simulation will be terminated after generating y-th population or after yielding output which is z times of Pth. 5. Job processing time, t is independent of the job sequence. 6. Machines will never breakdown and are available throughout the scheduling period. 7. Machine setup time is negligible. 8. Theoretical cycle time, Cth and total idle time, Ith are calculated considering the largest task time, t max as theoretical cycle time, Cth. 9. Daily production rate, Pth are calculated considering that all the operators are 100% efficient. 10. Tasks are assigned in workstations according to longest task time and the largest task time, t max is considered as theoretical cycle time, Cth. 4. GENETIC ALGORITHM APPROACH Genetic algorithm is based on the heuristic concept for solving complex optimization problems which is based on manipulating a population of solutions by genetic operators like selection, crossover and mutation. The main challenge of GA application to the assembly line balancing problem is the development of good encoding schemes and genetic operators in order to attain feasible solutions. Fig. 1: A Typical Scenario of Task Assignment in Assembly Line 3. ASSUMPTIONS OF THE STUDY Assumptions of operator assignment in a simple assembly line balancing problem (SALBP) are as follows: 1. Only one operator is assigned in each workstation. 2. Operator s skill is task independent. 3. Each entity of skill matrix represents the percentage of average task time taken to complete that particular task in that particular machine. An average operator takes 100% of task time to complete that task, where a skilled one takes less time to perform. 4. The number of workers assigned in each machine needs to be decided before any job can be processed and they will not be reassigned until all the jobs have been completed. 4.1 Representation Scheme Each chromosome is a string of length M (number of workstations) where each element represents a workstation and the value of each element represents the skill combination of operator of value h from skill matrix. For example, the first element of the chromosome, 2 means the operator who has skill combination of type 2, is assigned in workstation 1. This representation of chromosome is shown in Table 1. Skill combination of type 2 means that the operator is the most efficient in handling machine type 3 and can complete a task using 80% of average task time. And he is the least efficient in machine type 2 as he takes 110% of average task time to complete a task using that machine. The skill matrix for different machine types and skill combinations is shown in Table 2. Table 1 Representation of Chromosome Chromosome 2 1 3 1 3 3 2 2 1 3 Workstation 1 2 3 4 5 6 7 8 9 10 Combination 2 1 3 1 3 3 2 2 1 3 type

4 Tanzina Zaman, Sanjoy Kumar Paul and Abdullahil Azeem 4.2 Fitness Function Table 2 Representation of Skill Matrix N / h m/c m/c m/c m/c type 1 type 2 type 3 type 4 Skill Combination 1 0.80 1.10 1.00 0.90 Skill Combination 2 0.90 1.10 0.80 1.00 Skill Combination 3 1.00 0.80 1.10 0.90 The chromosome is selected on the basis of a fitness function which is dependent on production rate (P), cycle time (C) and total idle time (I). Production rate, P = daily available time x max Where, x max = highest task time after assignment of operator in workstation Cycle time, C = x max Total idle time, I = m i = 1 x max t wsm Where, t wsm = total task time of workstation m. If priority on production rate (P), cycle time (C) and total idle time (I) be w 1, w 2 and w 3 respectively, then the fitness function will be Fitness value = P w 1 + w 2 /C + w 3 /I The chromosome with the highest fitness value will be considered a better one. 4.3 Selection and Genetic Operators First initial population is initiated where random citizens are generated. Then parents are selected from population using roulette wheel which increases the probability of selecting the citizen having better fitness as a parent. Two genetic operators are used here; crossover and mutation. During crossover two parents are selected randomly and crossover point is generated from 1 to M. The child with better fitness value is kept and the other one is discarded. The crossover probability is 1.0. The other operator is mutation whose probability is 0.5. During mutation, the child survived after crossover is selected and mutation point is generated from 1 to M. 4.4 Termination Criteria The simulation will be terminated after generating y-th population or after yielding output which is z times of Pth which comes first. 5. DETERMINATION OF OPERATOR ASSIGNMENT USING GA In this work, genetic algorithm is used to reduce the computational complexities and furthermore, all possible optimal solutions can be judged. It is assumed that jobs are already assigned to workstations. Several input variables, e.g. number of workstations, types and number of machines in each workstation, task performed in each machine in each workstations, average task time, range of desired efficiency, dimension of skill matrix, range of operators skill, population size, termination criteria etc. First theoretical cycle time, Cth, total idle time, Ith and daily production rate, Pth are calculated assuming that each operator assigned in each workstation can complete the respective task utilizing fully the average task time. This means that operators are considered primarily having the equal capability to operate each machine. But if their capability is found to be machine dependent, the scenario would be different. The possible skill combinations are represented by skill matrix of dimension h N. The operator with suitable combination of skill is assigned in workstation. 6. RESULT ANALYSIS The algorithm developed for operator assignment in assembly line using GA, is coded in C++ programming language. Genetic algorithm is used here to verify all the possible combinations of operator assignment and to get the optimum solution which will indicate the optimum skill level of operator and their assignment in workstations. A case study is presented here where GA is used to assign operator. Hypothetical data is used here to represent a simple assembly line balancing problem. Nineteen tasks are performed in four types of machine to get a completed job. Nineteen tasks are assigned in ten workstations according to the longest task time rule. Separate machine is provided for each task. Depending upon the ability to operate a particular type of machine, skill combination of operator is varied. The schematic flow diagram of the considered assembly line in presented in Fig. 2 and the product flow through workstations are shown in Fig. 3.

Optimal Operator Assignment in an Assembly Line using Genetic Algorithm 5 In this case study, it is considered that workers work in an eight hour shift and 50 minutes is considered for down time. So, at 100% working efficiency, available time for a day is 25800 seconds. At 80% working efficiency, Maximum possible output, Pth = 516 pcs Cycle time, Cth = 40 seconds Total idle time, Ith = 93 seconds Moreover, the set of operator efficiency depending on operating a particular machine is considered, A = {85%, 95%, 100%, 110%, 120%}. Fig. 2: Precedence Diagram of Assembly Line Fig. 3: Schematic Diagram of Product Flow Through Workstations The Table 3 summarizes the tasks assigned in workstations, individual task data, total idle time for each station and the type of machine by which they are processed, in this case study. The task data can be obtained from any company's production department which is generally recorded after a detailed time study and in this case study, cycle time is considered as the largest task time, as assumed before. Table 3 Information About Tasks in Different Workstations WS Task Task Machine Idle number number time type time/ws 1 14 1 1 3 10 2 2 4 14 2 2 18 4 22 5 15 0 3 6 25 3 7 8 4 4 13 10 2 22 8 14 5 9 18 2 8 10 15 6 11 10 2 5 12 10 3 7 14 30 1 10 8 15 40 3 0 16 13 2 9 19 10 3 17 17 20 1 10 18 13 4 7 In this case study, three different situations are considered where maximization of productivity, decrease in cycle time and minimization of total idle time is given the most preference respectively. In this simulation, five chromosomes are generated in each generation, 150 populations will be generated before termination if 1.5 times of Pth is not achieved. 6.1 Situation 1; Maximization of Productivity (P) For w 1 = 7, w 2 = 1, w 3 = 1, the following results are obtained using the developed algorithm. Best fitted chromosome is 2 1 4 4 1 1 1 4 2 1, with a fitness value = 4249.46, where skill combination matrix is shown in Table 4. Table 4 Skill Combination Matrix for Maximization of Productivity Skill Machine Machine Machine Machine combination type 1 type 2 type 3 type 4 1 1.10 0.95 1.00 0.85 2 0.95 0.85 1.20 1.00 3 1.10 1.20 0.95 1.00 4 1.00 1.20 0.85 0.95 In this situation, P calculated = 607.06pcs, productivity increased by 17.647% C calculated = 34 seconds, decreased by 15% I calculated = 50.15 seconds, decreased by 46.075% As obtained in simulation, the first gene (2) of the best fitted chromosome represents that, in workstation 1 (WS 1) that operator should be assigned who has skill combination of type 2 to

6 Tanzina Zaman, Sanjoy Kumar Paul and Abdullahil Azeem achieve the above mentioned results. It means that he/she should take 95% of the task time to complete a task using machine type 1, take 85% of the task time using machine type 2, 120% of task time using machine type 3 and 100% of that using machine type 4. From this, it can be understood that WS1 requires an operator who is the most efficient in handling machine type 2. Similar representations for the rest of the genes of the chromosome can be obtained. 6.2 Situation 2; Minimization of Cycle Time (C) For w 1 = 1, w 2 = 7, w 3 = 1, following results are obtained using the developed algorithm. Best fitted chromosome is 3 4 4 3 2 3 4 4 1 3, with a fitness value = 607.28, where skill combination matrix is shown in Table 5. Table 5 Skill Combination Matrix for Minimization of Cycle Time Skill Machine Machine Machine Machine combination type 1 type 2 type 3 type 4 1 1.10 0.95 1.20 1.00 2 1.20 0.85 1.10 0.95 3 0.95 0.85 1.20 1.00 4 1.10 0.95 0.85 1.20 In this situation, P calculated = 607.06pcs, productivity increased by 17.647% C calculated = 34 seconds, decreased by 15% I calculated = 50.04 seconds, decreased by 46.194% 6.3 Situation 3; Minimization of Total Idle Time (I) For w 1 = 0.5, w 2 = 1, w 3 = 8, using the same algorithm the following results are obtained. Best fitted chromosome is 2 2 3 3 1 2 4 3 3 4, with a fitness value = 300.63, where skill combination matrix is shown in Table 6. Table 6 Skill Combination Matrix for Minimization of Idle Time Skill Machine Machine Machine Machine combination type 1 type 2 type 3 type 4 1 1.20 1.00 1.10 0.95 2 0.95 0.85 1.00 1.20 3 1.20 1.10 0.85 1.00 4 1.10 1.20 0.85 0.95 In this situation, P calculated = 600.87pcs, productivity increased by 16.448% C calculated = 34.35 seconds, decreased by 14.125% I calculated = 47.8 seconds, decreased by 48.6% 7. CONCLUSION The operator assignment problem in an assembly line has been considered in this research where optimized result was obtained checking possible solutions using genetic algorithm. Objectives like maximization of productivity, minimization of cycle time and minimization of total idle time have been considered to choose the optimized assignment, while is has been assumed that operators skill is machine dependent and task independent. Situations can be different depending on the priority given upon productivity, cycle time and idle time. When a particular factor is considered as prime concern, more priority is given on that factor in the fitness function. Chromosome with maximum fitness value is considered as optimum operator assignment. A particular chromosome represents the assignment of operators having a particular skill combination in a number of workstations in assembly line. Each element of the chromosome is referred to the skill matrix. As an operator is not equally efficient in operating each machine, his efficiency is represented by skill combination in operating different machines. The optimal assignment of operators is represented by the best fitted chromosome. This work can be extended considering operators efficiency on completing tasks and operating machines as well. REFERENCES [1] Anderson, E.J. and Ferris, M.C. (1994). Genetic Algorithms for Combi-natorial Optimization: The Assembly Line Balancing Problem, ORSA Journal on Computing, 6, pp. 161-173. [2] Baybars, I. (1986). A Sur vey of Exact Algorithms for the Simple Assembly Line Balancing Problem, Management Science, 32, pp. 909-932. [3] Baykaso ğ lu, A. and Özbak ı r, L. (2007). Stochastic U-line Balancing Using Genetic Algorithms, International Journal of Advanced Manufacturing Technology, 32 (1-2), pp. 139-147. [4] Becker C., and Scholl A., (2006). A Survey on Problems and Methods in Generalized

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