A simplified swarm optimization algorithm to minimize makespan on non-identical parallel machines with unequal job release times under non-renewable resource constraints

This article studies a uniform parallel machine scheduling problem with unequal job release times. It is assumed that each machine consumes a certain non-renewable resource when manufacturing jobs. The objective is to find an optimal schedule to minimize the makespan, given that the total resource consumption does not exceed the given limit. A mathematical model is first built to derive optimal solutions for small-scale instances. For large-scale instances, a simplified swarm optimization (SSO) algorithm is proposed. Considering that the parameters of meta-heuristic algorithms have great impacts on the output solution, the Taguchi method is then applied to tune the algorithm parameters. Afterward, a large number of simulation experiments are conducted. Finally, Friedman’s test and Wilcoxon signed-rank test are employed to analyze the simulation results from statistical perspectives. Experimental results reveal that the proposed algorithm can provide competitive solutions.