Bi-objective optimisation for scheduling the identical parallel batch-processing machines with arbitrary job sizes, unequal job release times and capacity limits

Abstract

This paper deals the scheduling identical parallel batch-processing machines (BPMs) that each machine can be process a group of jobs as a batch simultaneously. The paper presents a new bi-objective-mixed integer linear programming model for BPM in which arbitrary job size, unequal release time and capacity limits are considered as realistic assumptions occur in the manufacturing environments. The objectives are to minimise the makespan and the total weighted earliness and tardiness of jobs (just in time). After developing a new bi-objective model, an ɛ-constraint method is proposed to solve the problem. This problem has been known as Np-hard. Therefore, two multi-objective optimisation methods, namely, fast non-dominated sorting genetic algorithm (NSGA-II) and multi-objective imperialist competitive algorithm (MOICA) are employed to find the pareto-optimal front for large-sized problems. The parameters of the proposed algorithms are calibrated using Response surface methodology (RSM) and the performances of the proposed algorithms on the problems of various sizes are analysed and the computational results clarify that MOICA outperform than NSGA-II in quality of solutions and computational time.