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The single machine CON problem with unavailability period

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  • Enrique Gerstl
  • Gur Mosheiov

Abstract

The classical CON problem focuses on scheduling jobs on a single machine sharing a common due-date. We study the CON problem with a given unavailability period. The basic problem (assuming linear job-independent costs and no idle times prior to or after the unavailability period) is easily shown to be NP-hard, and an efficient pseudo-polynomial dynamic programming algorithm is introduced. Extensions of the algorithm to general monotonic job-independent costs, and to linear job-dependent costs are studied as well. All algorithms are tested numerically, and are shown to produce optimal schedules in reasonable time. Then we allow idle times, verify that this case is NP-hard in the ordinary sense as well, and introduce a greedy-type heuristic. Numerical tests are performed, and the results indicate that the heuristic performs extremely well.

Suggested Citation

  • Enrique Gerstl & Gur Mosheiov, 2021. "The single machine CON problem with unavailability period," International Journal of Production Research, Taylor & Francis Journals, vol. 59(3), pages 824-838, February.
    • Handle: RePEc:taf:tprsxx:v:59:y:2021:i:3:p:824-838
    DOI: 10.1080/00207543.2019.1709672
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    Cited by:

    1. Sang, Yao-Wen & Wang, Jun-Qiang & Sterna, Małgorzata & Błażewicz, Jacek, 2023. "Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work," Omega, Elsevier, vol. 121(C).
    2. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.

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