Iterative determination and matching of part groups and machine cells: Optimization and successive approximations

In the literature of production engineering the terminology ‘group technology’ is taken to indicate the formation of part groups that expedite and economize production, while ‘cellular manufacturing’ refers to the creating of subsets of machaines whose essential autonomy and simplicity is intended to yield similar rewards. Ordinarily, though relevant to the identical objectives, the two problems have been approached separately. The present paper develops mathematical formulations of these coupled problems and a computationally feasible, iterative algorithm for solving both within a single procedure. While groups and cells are built up successively and heuristically, the formulational effort is upon the group to cell assignment problem, the sequence of optimal solutions to which drives the successive approximations. Fairly loose assumptions eliminate the complexity of the discrete programming problems that result, and nothing beyond linear programming is required. The impact upon problem structure of the realities of the manufacturing environment is discussed.