Optimal solution of cellular manufacturing system design: Benders' decomposition approach

In this paper, a mathematical model for cellular manufacturing system design which incorporates three critical aspects – resource utilization, alternate routings, and practical constraints – is presented. The model is shown to be NP-complete. A linear, mixed-integer version of the model which not only has fewer integer variables compared to most other models in the literature, but one that also permits us to solve it optimally using Benders' decomposition approach is presented. Some results that allow us to solve the problem efficiently as well as computational results with Benders' decomposition algorithm and a modified version are presented.