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Scheduling parallel batching machines in a sequence

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  • Ward Passchyn
  • Frits Spieksma

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 bi-directional 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 Spieksma, 2016. "Scheduling parallel batching machines in a sequence," Working Papers of Department of Decision Sciences and Information Management, Leuven 555947, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    • Handle: RePEc:ete:kbiper:555947
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    Keywords

    Machine scheduling; Complexity; Parallel batching machine; Machine sequence;
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