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Minimizing the makespan on a single machine subject to modular setups

Author

Listed:
  • Dirk Briskorn

    (Bergische Universität Wuppertal, Professur für BWL, insbesondere Produktion und Logistik)

  • Konrad Stephan

    (Friedrich-Schiller-Universität Jena, Lehrstuhl für Operations Management)

  • Nils Boysen

    (Friedrich-Schiller-Universität Jena, Lehrstuhl für Operations Management)

Abstract

Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries. Solving this problem under the min-makespan objective is well known to be strongly NP-hard. We consider a special case of the problem arising from products having a modular design. This means that product characteristics, (mass-)customizable by customers, are realized by separate components that can freely be combined. If consecutive products differ by a component, then a setup is necessary. This results in a specially structured setup matrix that depends on the similarities of product characteristics. We differentiate alternative problem cases where, for instance, the setup operations for multiple components either have to be executed sequentially or are allowed to be conducted in parallel. We analyze the computational complexity of various problem settings. Our findings reveal some special cases that are solvable in polynomial time, whereas most problem settings are shown to remain strongly NP-hard.

Suggested Citation

  • Dirk Briskorn & Konrad Stephan & Nils Boysen, 2022. "Minimizing the makespan on a single machine subject to modular setups," Journal of Scheduling, Springer, vol. 25(1), pages 125-137, February.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:1:d:10.1007_s10951-021-00704-8
    DOI: 10.1007/s10951-021-00704-8
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    References listed on IDEAS

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    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
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