A NSGA-II and NSGA-III comparison for solving an open shop scheduling problem with resource constraints

This paper presents an open shop scheduling problem based on a real mechanical workshop made of m machines that process n jobs. It deals with different resource constraints related to the tools allocation and the multi-skills staff assignment. Resource skills and their availability are required to execute one process task. In this work, we expose a multi-objective problem where the idea is to minimize three objectives simultaneously. The first one considers the minimization of the total flow time of jobs in the production system, then the workload balancing concerning both, humans and machines is addressed. We propose and compare two multi-objective methods: NSGA-II and NSGA-III. Computational experiments are designed according to the literature, we expose the small and large sized instances to present the general performance of these algorithms using the hyper-volume metric to compare them.