Uniform parallel machine scheduling with fuzzy processing times under resource consumption constraint

Abstract

In this paper we consider a problem of scheduling n single-operation jobs on m uniform parallel machines. It is assumed that each machine has a resource consumption per unit time when processing the job. Our goal is to find a schedule that minimizes the makespan, subject to the constraint that the total resource consumption cannot exceed a given number. For solving this problem, a fuzzy simplified swarm optimization (SSO) algorithm, accompanied by a specific legalizing method, which is presented to legalize the infeasible solution, is employed. In order to verify the effectiveness and efficiency of this algorithm, we compare its performance with those of a genetic algorithm (GA) and a particle swarm optimization with genetic local search (PSOLS) both adapted from the literature. Considering the parameter values of algorithms have a great influence on the quality of the output solution, we first use Taguchi method to determine suitable levels for the design factors. Afterwards, three different job-scale simulated experiments (i.e., small, medium and large experiments) are separately conducted. Finally, to further analyze the level of difference between SSO and the other two algorithms, the Wilcoxon signed-rank test is carried out. Experimental results indicate that SSO performs better than GA and PSOLS.