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Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

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  • Simon Thevenin
  • Nicolas Zufferey
  • Jean-Yves Potvin

Abstract

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.

Suggested Citation

  • Simon Thevenin & Nicolas Zufferey & Jean-Yves Potvin, 2017. "Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1588-1606, March.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:6:p:1588-1606
    DOI: 10.1080/00207543.2016.1181285
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    Cited by:

    1. Julio Mar-Ortiz & Alex J. Ruiz Torres & Belarmino Adenso-Díaz, 2022. "Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier," Operational Research, Springer, vol. 22(4), pages 4585-4605, September.
    2. Hanane Krim & Nicolas Zufferey & Jean-Yves Potvin & Rachid Benmansour & David Duvivier, 2022. "Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times," Journal of Scheduling, Springer, vol. 25(1), pages 89-105, February.
    3. Santini, Alberto & Bartolini, Enrico & Schneider, Michael & Greco de Lemos, Vinicius, 2021. "The crop growth planning problem in vertical farming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 377-390.

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