A mathematical model and genetic algorithm to cyclic flexible job shop scheduling problem

Abstract

Product orders are usually released with a cyclic manner, in the part manufacturing industries. Hence, scheduling cyclic jobs instead of single jobs is more practical in the real manufacturing environment. In this paper, a flexible job shop scheduling problem with cyclic jobs is studied. In this problem, jobs must be delivered in determined batch sizes with definite time intervals. This problem is practical for many manufacturing systems such as automotive parts making industries. Whereas jobs are repeating infinitely during time, a framework is suggested to break down the infinite programming horizon to smaller periods. Then a mixed integer linear programming (MILP) model is presented to schedule jobs in this short term horizon. The goal of the proposed model is minimizing the total cost including delay costs, setup costs and holding costs. Since the problem is well-known as NP-hard class, the proposed MILP model is effective just for small size problems. Therefore, two algorithms based on genetic and simulated annealing (SA) algorithms are developed to solve real size problems. The numerical experiments are used to evaluate the performance of the developed algorithms. Results show that the proposed genetic algorithm (GA) has a better performance than the SA algorithm. Also some intelligent approaches are presented and examined in the proposed algorithms. Results show the efficiency of the presented intelligent approaches as mutation operators for the proposed GA.