A matheuristic based solution approach for the general lot sizing and scheduling problem with sequence dependent changeovers and back ordering

This paper considers the general lot sizing and scheduling problem (GLSP) in single level capacitated environments with sequence dependent item changeovers. The proposed model simultaneously determines the production sequence of multiple items with capacity-constrained dynamic demand and lot size to minimize overall costs. First, a mixed-integer programming (MIP) model for the GLSP is developed in order to solve smaller size problems. Afterwards, a matheuristic algorithm that integrates Simulated Annealing (SA) algorithm and the proposed MIP model is devised for solving larger size problems. The proposed matheuristic approach decomposes the GLSP into sub-problems. The proposed SA algorithm plays the controller role. It guides the search process by determining values for some of the decision variables and calls the MIP model to identify the optimal values for the remaining decision variables at each iteration. Extensive numerical experiments on randomly generated test instances are performed in order to evaluate the performance of the proposed matheuristic method. It is observed that the proposed matheuristic based solution method outperforms the MIP and SA, if they are used alone for solving the present GLSP.