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Scheduling parallel batching machines in a sequence

Author

Listed:
  • Ward Passchyn

    (KU Leuven
    OM Partners)

  • Frits C. R. Spieksma

    (KU Leuven
    Eindhoven University of Technology)

Abstract

Motivated by the application of scheduling a sequence of locks along a waterway, we consider a scheduling problem where multiple parallel batching machines are arranged in a sequence and process jobs that travel along this sequence. We investigate the computational complexity of this problem. More specifically, we show that minimizing the sum of completion times is strongly NP-hard, even for two identical machines and when all jobs travel in the same direction. A second NP-hardness result is obtained for a different special case where jobs all travel at an identical speed. Additionally, we introduce a class of so-called synchronized schedules and investigate special cases where the existence of an optimum solution which is synchronized can be guaranteed. Finally, we reinforce the claim that bidirectional travel contributes fundamentally to the computational complexity of this problem by describing a polynomial time procedure for a setting with identical machines and where all jobs travel in the same direction at equal speed.

Suggested Citation

  • Ward Passchyn & Frits C. R. Spieksma, 2019. "Scheduling parallel batching machines in a sequence," Journal of Scheduling, Springer, vol. 22(3), pages 335-357, June.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:3:d:10.1007_s10951-018-0560-6
    DOI: 10.1007/s10951-018-0560-6
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    References listed on IDEAS

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    1. Passchyn, Ward & Briskorn, Dirk & Spieksma, Frits C.R., 2016. "Mathematical programming models for lock scheduling with an emission objective," European Journal of Operational Research, Elsevier, vol. 248(3), pages 802-814.
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    6. Douglas Smith, L. & Nauss, Robert M. & Mattfeld, Dirk Christian & Li, Jian & Ehmke, Jan F. & Reindl, M., 2011. "Scheduling operations at system choke points with sequence-dependent delays and processing times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 669-680, September.
    7. Passchyn, Ward & Coene, Sofie & Briskorn, Dirk & Hurink, Johann L. & Spieksma, Frits C.R. & Vanden Berghe, Greet, 2016. "The lockmaster’s problem," European Journal of Operational Research, Elsevier, vol. 251(2), pages 432-441.
    8. Peter Brucker & Sigrid Knust & T.C. Cheng & Natalia Shakhlevich, 2004. "Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays," Annals of Operations Research, Springer, vol. 129(1), pages 81-106, July.
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