A linear formulation of the machine-part cell formation problem

The machine-part group formation is an important issue in the design of cellular manufacturing systems. The present paper first discusses some of the alternative formulations of this problem, their advantages and disadvantages, and then suggests a new linear zero-one formulation which seems to have removed most of the disadvantages observed in other models. It will be shown that most of the integrality conditions of the proposed formulation can be relaxed. This considerably improves its computational feasibility and efficiency. Finally, a simulated annealing approach to deal with large-scale problems is also presented.