A goal programming approach to the cell formation problem

Cellular manufacturing is employed to achieve efficiencies in production by exploiting similarities inherent in the production of parts. Specifically, parts with similar processing requirements are identified and the equipment necessary to process these groups of parts is identified and located together. Several important design objectives associated with cellular manufacturing are to: 1) reduce setup times, 2) produce parts cell complete, i.e., minimize intercellular movements of parts, 3) minimize investment in new equipment, and 4) maintain acceptable machine utilization levels. The goal of this research was to develop a cell formation procedure that directly addressed these design objectives. To achieve this, three goal programming models were developed corresponding to three unique situations: (1) setting up an entirely new system and purchasing all new equipment, (2) reorganizing the system using only existing equipment, and (3) reorganizing the system using existing equipment and some new equipment. Several assumptions were made in the development of the goal programming models. First, it was assumed that each part has a fixed routing. Also, it was assumed that the processing times for the parts at each machine, the demand for each part, and the capacity and cost of each machine were known. In addition it was assumed that a given machine type could be placed in more than one cell and that the sequence in which the parts are processed affects setup times. Finally, it was assumed that a batch of each part is produced every production cycle and that only one batch of parts is processed in a particular cell at any givne time. Clearly defining the objectives and constraints associated with the cell formation problem is the major contribution of the three formulations. Correct identification of the problem and the relationships inherent to cellular manufacturing is a necessary first step in the decision process that heretofore has not received adequate attention. However, because of the large number of 0/1 variables contained in the goal programming formulations they are very difficult to solve for realistically-sized problems. Thus, a heuristic solution procedure is presented. The heuristic solution procedure involved partitioning the goal programming formulations into two subproblems and solving them in successive stages. A numerical example is presented that illustrates the two-stage heuristic procedure.