Comparison of objective criteria for set-up planning in complementary flexible manufacturing systems

A variety of objective criteria are used in optimizing the flexible manufacturing system set-up problem in the academic literature. The literature also provides evidence that the objective criteria used in academic studies are often the least important in practice and that inventory related costs are rarely considered as an objective criterion. This study compares the flexible manufacturing system set-up problem across a set of strategically selected objective criteria including an inventory cost criterion. The comparison is done over varying set-up costs to inventory carrying cost ratios and machine workloads. The study provides guidelines on the merits of using each objective criterion under different conditions. The models used in the study included large mixed integer programming problems and quadratic programming problems with continuous and binary variables present. The binary variables in the quadratic program give the problem a combinatorial nature. In order to circumvent the combinatorial nature of the problem, we have used a combination of generate-and-test and constraint propagation strategies to generate the feasible values of the binary variables at the constraint level and to propagate the feasible binary values into the models. Generate-and-test and constraint propagation strategies used in conjunction with mathematical programming are shown to greatly simplify generating solutions to a family of problems that are otherwise considered intractable.