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Online algorithms to schedule a proportionate flexible flow shop of batching machines

Author

Listed:
  • Christoph Hertrich

    (Technische Universität Kaiserslautern
    Technische Universität Berlin)

  • Christian Weiß

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Heiner Ackermann

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Sandy Heydrich

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Sven O. Krumke

    (Technische Universität Kaiserslautern)

Abstract

This paper is the first to consider online algorithms to schedule a proportionate flexible flow shop of batching machines (PFFB). The scheduling model is motivated by manufacturing processes of individualized medicaments, which are used in modern medicine to treat some serious illnesses. We provide two different online algorithms, proving also lower bounds for the offline problem to compute their competitive ratios. The first algorithm is an easy-to-implement, general local scheduling heuristic. It is 2-competitive for PFFBs with an arbitrary number of stages and for several natural scheduling objectives. We also show that for total/average flow time, no deterministic algorithm with better competitive ratio exists. For the special case with two stages and the makespan or total completion time objective, we describe an improved algorithm that achieves the best possible competitive ratio $$\varphi =\frac{1+\sqrt{5}}{2}$$ φ = 1 + 5 2 , the golden ratio. All our results also hold for proportionate (non-flexible) flow shops of batching machines (PFB) for which this is also the first paper to study online algorithms.

Suggested Citation

  • Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2022. "Online algorithms to schedule a proportionate flexible flow shop of batching machines," Journal of Scheduling, Springer, vol. 25(6), pages 643-657, December.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:6:d:10.1007_s10951-022-00732-y
    DOI: 10.1007/s10951-022-00732-y
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    References listed on IDEAS

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