Multi-objective Mixed Model Assembly Line Sequencing Optimization Using an Interactive Fuzzy Algorithm

In practice, vagueness and impreciseness of the goals in multi-objective mixed model assembly line make the decisionmaking a complex task. To limit the influences of the decision makers’ incomplete knowledge about the problem and help them to concentrate better on evaluating a conceived solution, a novel interactive fuzzy goal programming (IFGP) algorithm is proposed. The algorithm controls the search direction via updating both the membership values and the aspiration levels while minimizing the total utility work and the total production rate variation simultaneously. The proposed approach adopts both piecewise linear and linear membership functions to represent the fuzzy goals of the decision maker for the integrated mixed model assembly line sequencing problem, and achieves an efficient compromise solution. INTRODUCTION Mixed model assembly lines (MMAL) are a type of production line where a variety of product models with similar characteristics are assembled. The effective utilization of a mixed model assembly line requires solving two problems in a sequential manner as follows: 1) line design and balancing and 2) determination of the production sequence for different models. In this paper, we assume that the line has already been balanced and only the sequencing problem is considered. Determining the sequence of models in the assembly line is particularly important considering the crucial goals for the efficient implementation of just-in-time (JIT) systems. Bard et al presented an analytical framework for a mixed-model assembly line sequencing problem in order to minimize the overall lenghth of the line [1]. Bautista and Cano [2] developed some useful procedure to solve the mixed-model assembly line sequencing problem proposed by Yano and Rachamdugu. They also compared their algorithms with others taken from literature using two computational experiments. Toksari et al. introduced learning effect into assembly line sequencing problem. They showed that with the consideration of learning effects both the simple assembly line balancing and the U-type line balancing problems would remain solvable [3]. Sequencing mixed-model assembly lines have also been studied as a multi-objective problem. Hyun et al. addressed three objectives minimizing total utility work, keeping a constant rate of part usage, and minimizing total setup cost. This problem was solved by proposing a new genetic evaluation and selection mechanism [4]. McMullen considered two objectives minimizing the number of setups and keeping a constant rate of part usage, and solved this problem by a Tabu Search (TS) method [5]. Korkmazel and Meral developed the weighted-sum approach for two goals introduced by Monden [6]. Mahdavi et al proposed a two-phase linear programming approach to solve multi-objective mixed-model assembly line problem [7]. In this paper a new interactive fuzzy goal programming algorithm is applied to problems where simultaneous minimization of the total utility work and the total production rate variation as objectives are desired. THE MULTI-OBJECTIVE MIXED MODEL ASSEMBLY LINE MODEL The MMAL considered in this paper is a conveyor system moving at a constant speed (vc). Similar products are launched onto the conveyor at a fixed rate. The line is partitioned into J stations. It is assumed that the stations are all closed types. A closed station has boundaries, which workers cannot cross. Such a closed station is often found in reality where the use of facilities is restricted within a certain boundary. The tasks allocated to each station are properly balanced and their operating times are deterministic. The worker moves downstream on the conveyor while performing his/her tasks to assemble a product. On completion of the job, the worker moves upstream to the next product. The worker’s moving time is assumed to be negligible compared to the processing times. The design of an MMAL involves several issues such as determining operator schedules, product mix and launch intervals. Two types of operator schedules, early start and late start, are found in [1] and used in this work. The minimum part or model set (MPS) production, a strategy widely accepted in mixed model assembly lines, is also used in this paper. MPS is a vector representing a product mix, such that (d1,...,dM) =(D1/h,...,DM/h). Considering that m shows the type of the model and M is the number of model types, Dm is the number of products of model type m that must be assembled during an entire planning horizon and h is the greatest common divisor or highest common factor of D1,D2,...,DM .This strategy operates in a cyclical manner. The number of products produced in one