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New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

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  • Prot, D.
  • Bellenguez-Morineau, O.
  • Lahlou, C.

Abstract

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems.

Suggested Citation

  • Prot, D. & Bellenguez-Morineau, O. & Lahlou, C., 2013. "New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria," European Journal of Operational Research, Elsevier, vol. 231(2), pages 282-287.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:2:p:282-287
    DOI: 10.1016/j.ejor.2013.05.041
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    References listed on IDEAS

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    1. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    2. Blazewicz, Jacek & Dror, Moshe & Weglarz, Jan, 1991. "Mathematical programming formulations for machine scheduling: A survey," European Journal of Operational Research, Elsevier, vol. 51(3), pages 283-300, April.
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    Cited by:

    1. Janiak, Adam & Janiak, Władysław A. & Krysiak, Tomasz & Kwiatkowski, Tomasz, 2015. "A survey on scheduling problems with due windows," European Journal of Operational Research, Elsevier, vol. 242(2), pages 347-357.
    2. Choo Jun Tan & Siew Chin Neoh & Chee Peng Lim & Samer Hanoun & Wai Peng Wong & Chu Kong Loo & Li Zhang & Saeid Nahavandi, 2019. "Application of an evolutionary algorithm-based ensemble model to job-shop scheduling," Journal of Intelligent Manufacturing, Springer, vol. 30(2), pages 879-890, February.
    3. Hui-Chih Hung & Bertrand M. T. Lin & Marc E. Posner & Jun-Min Wei, 2019. "Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs," Journal of Scheduling, Springer, vol. 22(4), pages 413-431, August.
    4. Miguel A. Ortíz & Leidy E. Betancourt & Kevin Parra Negrete & Fabio Felice & Antonella Petrillo, 2018. "Dispatching algorithm for production programming of flexible job-shop systems in the smart factory industry," Annals of Operations Research, Springer, vol. 264(1), pages 409-433, May.
    5. Yabo Luo, 2017. "Nested optimization method combining complex method and ant colony optimization to solve JSSP with complex associated processes," Journal of Intelligent Manufacturing, Springer, vol. 28(8), pages 1801-1815, December.

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