Robust Parallel Machine Scheduling Problem with Uncertainties and Sequence-Dependent Setup Time

A parallel machine scheduling problem in plastic production is studied in this paper. In this problem, the processing time and arrival time are uncertain but lie in their respective intervals. In addition, each job must be processed together with a mold while jobs which belong to one family can share the same mold. Therefore, time changing mold is required for two consecutive jobs that belong to different families, which is known as sequence-dependent setup time. This paper aims to identify a robust schedule by min-max regret criterion. It is proved that the scenario incurring maximal regret for each feasible solution lies in finite extreme scenarios. A mixed integer linear programming formulation and an exact algorithm are proposed to solve the problem. Moreover, a modified artificial bee colony algorithm is developed to solve large-scale problems. The performance of the presented algorithm is evaluated through extensive computational experiments and the results show that the proposed algorithm surpasses the exact method in terms of objective value and computational time.