A new model for integrated lot sizing and scheduling in flexible job shop problem

In this paper an integrated lot-sizing and scheduling problem in a flexible job shop environment with machine-capacity-constraint is studied. the main objective is to minimize the total cost which includes the inventory costs, production costs and the costs of machine’s idle times. first, a new mixed integer programming model, with small bucket time approach, based on proportional lot sizing and scheduling problems (plsp), is proposed to formulate the problem. since the problem under study is np-hard, a modified harmony search algorithm, with a new built-in local search heuristic is proposed as solution technique. in this algorithm, it is improvised a new harmony vector in two phases to enhance search ability. additionally, taguchi method is used to calibrate the parameters of the modified harmony search (hs) algorithm. finally, comparative results demonstrate the effectiveness of the modified harmony search algorithm in solving the problem.it is also demonstrated that the proposed algorithm can find good quality solutions for all size problems. the objective values obtained by proposed algorithm are better from hs algorithm and exact method results.