Product sequencing problem in Mixed-Model Assembly Line to minimize unfinished works

Abstract

This study is concerned about how to optimize the input sequence of product models with sequence-dependent setup time in Mixed-Model Assembly Line (MMAL) using conveyor system. Usually MMAL consists of a number of stations linked by a conveyor belt and each station has a work zone limited by upstream and down stream boundaries. To avoid improper interference between operators in the adjacent stations and excess of machine moving range, operators are forced to complete their operations within their predetermined work zone. In this study, our goal is to determine the sequence of models for minimizing the total unfinished work within their work zone. A generalized formulation of the product sequencing problem in MMAL is presented. We developed an optimal procedure using Branch & Bound technique and a heuristic procedure using lower bound and local search. Experimental results show that the heuristic procedure provides reasonably good solutions with low computational costs.

Introduction

Mixed-Model Assembly Line (MMAL) is known to be a special case of production lines where various and different models of the same product are inter-mixed to be assembled on the same line (Moden, 1983). MMAL is widely used in many manufacturing systems – from consumer electronics to automotive manufacturing – for meeting the diversified demands of customers without large end product inventories. In MMAL, products are transported on conveyor belt and operators move along with the belt while working on a product. An operator can work on a product only when it is within his/her work zone limited by upstream and downstream boundaries. So, there may be many cases that the operator cannot finish work on a product before it leaves his/her station (Tsai, 1995). Related to MMAL environments, many research works are found on the problem of sequencing models to minimize the variation of production rates where a suitable mixed-model balance has already been achieved and the conveyor should not be stopped (Steiner and Yeomans, 1993, Miltenburg and Sinnamon, 1992, Cheng and Ding, 1996). This paper is concerned with the problem of minimizing the total unfinished works in MMAL. This study is meaningful in that in real manufacturing environments keeping the suitable mixed-model balance is very difficult and minimizing the unfinished works is a very practical goal.

Xiaobo and Ohno, 1994, Xiaobo and Ohno, 1997 proposed a branch-and-bound method for finding an optimal or sub-optimal sequence of mixed models that minimizes the total conveyor stoppage time. Sarker and Pan (1998) developed two models for closed and open-station in order to minimize the total cost of the utility time and idle time. Yano and Rachamadugu (1991) dealt with the problem of sequencing jobs with customer-specified options to minimize the total amount of incomplete works. Bolat (1997) also addressed the problem of minimization of the remaining works in a paced assembly line. However, all the previous works assume that there is no setup time between models or even the setup times are independent of sequences of models. Even though Bolat, 1994, Bolat et al., 1994 considered a sequencing problem with sequence-dependent setup costs, the setup costs are assumed to be independent of the completion time of the model.

This paper is focused on the problem of how to sequence jobs with sequence-dependent setup to minimize the total unfinished works. For this problem, we constructed a mathematical model and proposed a branch-and-bound algorithm and a heuristic procedure for finding practically a good solution.