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Single-machine batch scheduling to minimize the total setup cost in the presence of deadlines

Author

Listed:
  • Dominik Kress

    (University of Siegen)

  • Maksim Barketau

    (National Academy of Sciences of Belarus)

  • Erwin Pesch

    (University of Siegen
    HHL Leipzig)

Abstract

We address the single-machine batch scheduling problem with the objective of minimizing the total setup cost. This problem arises when there are n jobs that are partitioned into F families and when setup operations are required whenever the machine switches from processing a job of one family to processing a job of another family. We assume that setups do not require time but are associated with a fixed cost which is identical for all setup operations. Each job has a processing time and an associated deadline. The objective is to schedule all jobs such that they are on time with respect to their deadlines and the total setup cost is minimized. We show that the decision version of this problem is NP-complete in the strong sense. Furthermore, we present properties of optimal solutions and an $$O(n\log n+nF)$$ O ( n log n + n F ) algorithm that approximates the cost of an optimal schedule by a factor of F. The algorithm is analyzed in computational tests.

Suggested Citation

  • Dominik Kress & Maksim Barketau & Erwin Pesch, 2018. "Single-machine batch scheduling to minimize the total setup cost in the presence of deadlines," Journal of Scheduling, Springer, vol. 21(6), pages 595-606, December.
    • Handle: RePEc:spr:jsched:v:21:y:2018:i:6:d:10.1007_s10951-018-0561-5
    DOI: 10.1007/s10951-018-0561-5
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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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    6. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
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    8. Lu, L.F. & Yuan, J.J., 2007. "The single machine batching problem with identical family setup times to minimize maximum lateness is strongly NP-hard," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1302-1309, March.
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    Cited by:

    1. Shaojun Lu & Jun Pei & Xinbao Liu & Xiaofei Qian & Nenad Mladenovic & Panos M. Pardalos, 2020. "Less is more: variable neighborhood search for integrated production and assembly in smart manufacturing," Journal of Scheduling, Springer, vol. 23(6), pages 649-664, December.
    2. Eduardo Queiroga & Rian G. S. Pinheiro & Quentin Christ & Anand Subramanian & Artur A. Pessoa, 2021. "Iterated local search for single machine total weighted tardiness batch scheduling," Journal of Heuristics, Springer, vol. 27(3), pages 353-438, June.

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