A genetic algorithm for integrated lot sizing and supplier selection with defective items and storage and supplier capacity constraints

The single product, multi-period inventory lot-sizing problem is one of the most common and basic problems in the production and inventory management literature. In this paper, we consider an environment with multiple suppliers and multiple periods with supplier capacity and storage capacity constraints. Moreover, considering defective items, we move one-step toward a real environment of inventory problems. In this paper, we present the nonlinear programming of the problem. Since complexity of lot sizing problems belongs to a class of NP-hard problems, we propose a genetic algorithm to solve the problem. We develop a unique encoding-decoding procedure, which creates feasible solutions. Using the Taguchi experimental design method, the optimum parameters of the proposed genetic algorithm are selected. The result comparison between proposed GA and GAMS software as an exact solution for small and medium size problems shows that we can trust the proposed GA as a solution methodology for larger problems.