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Single machine scheduling problems with generalised due-dates and job-rejection

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  • Enrique Gerstl
  • Gur Mosheiov

Abstract

We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.

Suggested Citation

  • Enrique Gerstl & Gur Mosheiov, 2017. "Single machine scheduling problems with generalised due-dates and job-rejection," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3164-3172, June.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:11:p:3164-3172
    DOI: 10.1080/00207543.2016.1266055
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    Citations

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    Cited by:

    1. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    2. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    3. Baruch Mor & Gur Mosheiov & Dana Shapira, 2021. "Single machine lot scheduling with optional job-rejection," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 1-11, January.
    4. 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.
    5. Baruch Mor & Gur Mosheiov, 2021. "A note: flowshop scheduling with linear deterioration and job-rejection," 4OR, Springer, vol. 19(1), pages 103-111, March.
    6. Baruch Mor & Gur Mosheiov & Dana Shapira, 2020. "Flowshop scheduling with learning effect and job rejection," Journal of Scheduling, Springer, vol. 23(6), pages 631-641, December.
    7. Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2021. "Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates," Journal of Scheduling, Springer, vol. 24(6), pages 553-567, December.
    8. Baruch Mor & Gur Mosheiov, 2018. "A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection," Annals of Operations Research, Springer, vol. 271(2), pages 1079-1085, December.
    9. 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.
    10. Baruch Mor & Gur Mosheiov, 2022. "Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection," Operational Research, Springer, vol. 22(3), pages 2707-2719, July.

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