A Bi-objective Model for Dual-resource Constrained Job Shop Scheduling with the Consideration of Energy Consumption

Abstract

Dual resource constrained job shop problem (DR-CJSP) is an extension of the job shop scheduling problem such that each job has two available processing resources like machines and workers, each of which is of a non-identical number of operations. In many real manufacturing systems, machines often process in different processing speeds for some special demands. Note that the processing time of each job not only depends on the assigned worker but also on deployed machine. This undoubtedly leads to non-deterministic job processing time, thus resulting in different electricity consumption. We investigate the bi-objective DRCJSP problem with multi-processing speed for minimizing makespan and total electricity consumption in this work. We establish a bi-objective integer programming model and devise an epsilon constraint algorithm together with a non-dominated sorting genetic algorithm II (NSGA-II). The epsilon constraint method produces exact solutions for small job instances while NSGA-II can efficiently solve large job instances. Numerical experiments validate the proposed model and algorithms.