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

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  • Fanjul-Peyro, Luis
  • Perea, Federico
  • Ruiz, Rubén

Abstract

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.

Suggested Citation

  • Fanjul-Peyro, Luis & Perea, Federico & Ruiz, Rubén, 2017. "Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources," European Journal of Operational Research, Elsevier, vol. 260(2), pages 482-493.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:2:p:482-493
    DOI: 10.1016/j.ejor.2017.01.002
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    References listed on IDEAS

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    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
    2. Fanjul-Peyro, Luis & Ruiz, Rubén, 2010. "Iterated greedy local search methods for unrelated parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 207(1), pages 55-69, November.
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    5. E. Mokotoff & J.L. Jimeno, 2002. "Heuristics Based on Partial Enumeration for the Unrelated Parallel Processor Scheduling Problem," Annals of Operations Research, Springer, vol. 117(1), pages 133-150, November.
    6. Kellerer, H. & Strusevich, V. A., 2003. "Scheduling parallel dedicated machines under a single non-shared resource," European Journal of Operational Research, Elsevier, vol. 147(2), pages 345-364, June.
    7. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    8. Edis, Emrah B. & Oguz, Ceyda & Ozkarahan, Irem, 2013. "Parallel machine scheduling with additional resources: Notation, classification, models and solution methods," European Journal of Operational Research, Elsevier, vol. 230(3), pages 449-463.
    9. Billaut, Jean-Charles & Della Croce, Federico & Grosso, Andrea, 2015. "A single machine scheduling problem with two-dimensional vector packing constraints," European Journal of Operational Research, Elsevier, vol. 243(1), pages 75-81.
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