Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources

• Published in: European journal of operational research Vol. 260; no. 2; pp. 482 - 493
• Main Authors: Fanjul-Peyro, Luis, Perea, Federico, Ruiz, Rubén
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.07.2017
• Subjects: Additional resources; Makespan; Matheuristics; Parallel machine problem; Scheduling; Parallel machine problem; Scheduling; Makespan; Additional resources; Matheuristics
• ISSN: 0377-2217; 1872-6860; 1872-6860
• DOI: 10.1016/j.ejor.2017.01.002

•The problem of unrelated parallel machines with an additional resource is considered.•Two mathematical models are proposed: one adapted from the literature, an original one based on strip packing.•Three matheuristic strategies are proposed.•A comprehensive computational and statistical evaluation is carried out.•The model based on strip packing is shown to outperform the model adapted from the literature.•Matheuristic strategies are able to solve larger problems more efficiently and effectively. In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature. The other one, which is based on the resemblance to strip packing problems, is an original contribution of this paper. As the models presented are incapable of solving medium-sized instances to optimality, we propose three matheuristic strategies for each of these two models. The algorithms proposed are tested over an extensive computational experience. Results show that the matheuristic strategies significantly outperform the mathematical models.