Solving a multi-objective open shop problem for multi-processors under preventive maintenance

This research considers an open shop scheduling problem with preventive maintenance. A specific level of reliability is assumed and a mathematical model is presented to schedule both production and maintenance tasks, simultaneously. Three different and conflicting objective functions containing machine availability, make-span, and total tardiness and earliness have been optimized in the proposed model. When there are more than two machines in the open shop problem, it is classified in the category of NP-hard problems. Consequently, classical approaches cannot reach to an optimal solution in a reasonable time. Thus, two well-known algorithms for multi-objective problems containing non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are developed to find the best near-optimal solutions. The surface response methodology (RSM) is applied to tune parameters of the developed algorithms. Then, the reliabilities of the presented algorithms are illustrated based on three evaluation metrics comprising the number of Pareto solutions, spacing, and diversity. Furthermore, the superiority of the proposed algorithms is shown through benchmarking approach. The algorithms may be used in other open shop problems because they are able to find the best and reliable near-optimal solutions in a reasonable processing time.