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Single Machine Scheduling Problems with General Breakdowns, Earliness and Tardiness Costs

Author

Listed:
  • A. Federgruen

    (Columbia University, New York)

  • G. Mosheiov

    (Hebrew University, Jerusalem, Israel)

Abstract

In this paper we consider single machine scheduling problems with a common due-date for all jobs, arbitrary monotone earliness and tardiness costs and arbitrary breakdown and repair processes. We show that the problem is equivalent to a deterministic one without breakdowns and repairs and with an equivalent cost function of a job's completion time. A V -shaped schedule without idle times is shown to be optimal, if this equivalent cost function is quasi-convex .Conversely, we show that a V -shaped schedule may fail to be optimal if the property does not apply. We derive general conditions for the earliness and tardiness cost structure and repair and breakdown processes under which the equivalent cost function is quasi-convex . When a V -shaped schedule is optimal, an efficient (though pseudo-polynomial) algorithm can be used to compute an optimal schedule.

Suggested Citation

  • A. Federgruen & G. Mosheiov, 1997. "Single Machine Scheduling Problems with General Breakdowns, Earliness and Tardiness Costs," Operations Research, INFORMS, vol. 45(1), pages 66-71, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:66-71
    DOI: 10.1287/opre.45.1.66
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    Citations

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    Cited by:

    1. Yarlin Kuo & Zi‐Ann Chang, 2007. "Integrated production scheduling and preventive maintenance planning for a single machine under a cumulative damage failure process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 602-614, September.
    2. Chen, Zhi-Long & Lee, Chung-Yee, 2002. "Parallel machine scheduling with a common due window," European Journal of Operational Research, Elsevier, vol. 136(3), pages 512-527, February.
    3. Luh, Peter B. & Liu, Feng & Moser, Bryan, 1999. "Scheduling of design projects with uncertain number of iterations," European Journal of Operational Research, Elsevier, vol. 113(3), pages 575-592, March.
    4. Sen, Tapan & Sulek, Joanne M. & Dileepan, Parthasarati, 2003. "Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey," International Journal of Production Economics, Elsevier, vol. 83(1), pages 1-12, January.
    5. G Mosheiov, 2003. "Scheduling unit processing time jobs on an m-machine flow-shop," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 437-441, April.
    6. Kerem Bülbül & Safia Kedad-Sidhoum & Halil Şen, 2019. "Single-machine common due date total earliness/tardiness scheduling with machine unavailability," Journal of Scheduling, Springer, vol. 22(5), pages 543-565, October.
    7. Mosheiov, Gur & Shadmon, Michal, 2001. "Minmax earliness-tardiness costs with unit processing time jobs," European Journal of Operational Research, Elsevier, vol. 130(3), pages 638-652, May.

    More about this item

    Keywords

    production/scheduling; stochastic;

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