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INTRODUCTION
The manufacture of clothing involves carrying out tasks in restricted sequences. Components are gathered into subassemblies, which are eventually collected into a final assembly. Conceptually, the problems faced are essentially the same as those encountered in all other discrete product manufacturing industries. Tasks or processes are carried out at workstations sometimes simultaneously. The set of workstations involved in the assembly of a product can be thought of as an assembly line. Balancing such lines concerns allocating tasks to workstations in such a manner as to apportion the assembly work among the stations as evenly as possible without violating any precedence requirements and without having the sum of the task times at any workstation exceeding the cycle time. Here the cycle time is the elapsed time for the production of one unit of the product.
Mathematically, the problem in its simplest form can be defined as a finite set of tasks Iota = 1, 2,...i, n to be performed on a product, each with a known execution time t sub i and a set of precedence constraints which govern the order in which assembly may be completed. The problem is how the tasks should be assigned to workstations such that the precedence constraints are satisfied, the cycle time is not exceeded and that some measure of effectiveness is optimized, such as minimizing the idle time at all workstations.
Considerable effort has been devoted to this problem, in order to obtain balances. Different techniques, both exact and heuristic, have appeared in the literature. Bowman 1! developed two separate integer linear programming models. An improved version of the technique is given by Patterson and Albracht 2!, while an alternative formulation as a general integer programming problem has been proposed by Talbot and Patterson 3!. Recently Kao and Queyranne 4! used a dynamic programming approach to solve this type of problem. Van Assche and Herroelen 5! constructed a frontier search method while Wee and Magazing 6! presented a branch and bound method. Johnson 7! also described a branch and bound algorithm which involved searching for the newest node. Helgeson and Birnie 8! proposed the ranked positional weight method, Arcus 9! used a probabilistic approach based on random activity selection which yielded feasible sequences. Hoffman 10! suggested a rule...