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Minmax scheduling problems with common due-date and completion time penalty

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  • Baruch Mor

    (Ariel University)

Abstract

We study the well-known common due-date assignment and scheduling problem and focus on minmax objective functions with position-dependent processing times. In due-date assignment problems, the objective is to find simultaneously the optimal job sequence and due-date that minimize the total earliness, tardiness and due-date related costs. Based on the solution of the problem with position-independent processing times, positional-weights are provided that lead to a simple solution procedure. Two extensions of the basic problem are discussed and solved to optimality. First, we generalize the results of the due-date to the setting of due-window assignment. Second, we study the common due-date problem with completion time penalty. The latter problem is studied with position-independent and position-dependent processing times as well as optional job rejection. For all studied problems, except the last, we introduce efficient polynomial time solutions. In respect to the last problem, considering job-rejection, we prove that it is NP-hard in the ordinary sense and provide an efficient pseudo-polynomial dynamic programming algorithm and extensive numerical study.

Suggested Citation

  • Baruch Mor, 2019. "Minmax scheduling problems with common due-date and completion time penalty," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 50-71, July.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0365-8
    DOI: 10.1007/s10878-018-0365-8
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    References listed on IDEAS

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    1. Hui Zhu & Min Li & Zhangjin Zhou & Yun You, 2016. "Due-window assignment and scheduling with general position-dependent processing times involving a deteriorating and compressible maintenance activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3475-3490, June.
    2. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    3. G Mosheiov & A Sarig, 2008. "A due-window assignment problem with position-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(7), pages 997-1003, July.
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    5. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    6. Shabtay, Dvir, 2014. "The single machine serial batch scheduling problem with rejection to minimize total completion time and total rejection cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 64-74.
    7. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    8. Alan Washburn & Moshe Kress, 2009. "Search," International Series in Operations Research & Management Science, in: Combat Modeling, chapter 0, pages 133-160, Springer.
    9. Biskup, Dirk, 1999. "Single-machine scheduling with learning considerations," European Journal of Operational Research, Elsevier, vol. 115(1), pages 173-178, May.
    10. Janiak, Adam & Janiak, Władysław A. & Krysiak, Tomasz & Kwiatkowski, Tomasz, 2015. "A survey on scheduling problems with due windows," European Journal of Operational Research, Elsevier, vol. 242(2), pages 347-357.
    11. 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.
    12. Gordon, Valery S. & Strusevich, Vitaly A., 2009. "Single machine scheduling and due date assignment with positionally dependent processing times," European Journal of Operational Research, Elsevier, vol. 198(1), pages 57-62, October.
    13. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.
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    Cited by:

    1. Baruch Mor & Gur Mosheiov, 2021. "A note on the single machine CON and CONW problems with lot scheduling," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 327-338, August.

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