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Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection

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Abstract

We study a single machine scheduling problem, where the goal is to maximize the weighted number of jobs completed exactly at their due-dates. The option of job-rejection is considered, i.e., the scheduler may perform only a subset of the jobs. An upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-hard, and a pseudo-polynomial dynamic programming algorithm is introduced. Our numerical tests indicate that the proposed algorithm performs well: medium size instances (of up to 100 jobs) are solved in less than 1 s.

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Acknowledgements

This research was supported by the Israel Science Foundation (Grant No. ISF 2505/19). The second author was also supported by the Charles I. Rosen Chair of Management, and by The Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.

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All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

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Authors and Affiliations

  1. Department of Economics and Business Administration, Ariel University, 40700, Ariel, Israel

    Baruch Mor

  2. School of Business Administration, The Hebrew University, 91905, Jerusalem, Israel

    Gur Mosheiov

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  1. Baruch Mor
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  2. Gur Mosheiov
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Correspondence to Gur Mosheiov.

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Mor, B., Mosheiov, G. Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection. Oper Res Int J 22, 2707–2719 (2022). https://doi.org/10.1007/s12351-021-00627-4

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  • DOI: https://doi.org/10.1007/s12351-021-00627-4

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