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Scheduling with regular performance measures and optional job rejection on a single machine

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  • Baruch Mor
  • Dana Shapira

Abstract

We address single machine problems with optional job rejection, and focus on minimizing regular performance measures, ie, functions that are non-decreasing in the jobs, completion times, subject to the constraint that the total rejection cost cannot exceed a predefined upper bound. Our contribution is twofold. First, we consider two problems that, to the best of our knowledge, were not addressed in scheduling theory – total (unweighted) tardiness with a common due date and total weighted tardiness with a common due date. For these problems, we show that they are NP-hard and present pseudo-polynomial-time dynamic programming (DP) solution algorithms. Second, we revisit three problems: makespan with release-dates, total completion time, and total weighted completion time, and present enhanced DP solution algorithms. To all studied problems, we provide extensive numerical studies, verifying their efficiency, subsequently demonstrating both theoretical and practical enhancement.

Suggested Citation

  • Baruch Mor & Dana Shapira, 2020. "Scheduling with regular performance measures and optional job rejection on a single machine," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(8), pages 1315-1325, August.
    • Handle: RePEc:taf:tjorxx:v:71:y:2020:i:8:p:1315-1325
    DOI: 10.1080/01605682.2019.1621222
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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.
    3. Guojun Hu & Pengxiang Pan & Suding Liu & Ping Yang & Runtao Xie, 2024. "The prize-collecting single machine scheduling with bounds and penalties," Journal of Combinatorial Optimization, Springer, vol. 48(2), pages 1-13, September.
    4. Matan Atsmony & Gur Mosheiov, 2023. "Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection," Journal of Scheduling, Springer, vol. 26(2), pages 193-207, April.

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