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New Lower and Upper Bounds for Scheduling Around a Small Common Due Date

Author

Listed:
  • J. A. Hoogeveen

    (Eindhoven University of Technology, Eindhoven, The Netherlands)

  • H. Oosterhout

    (Tilburg University, Tilburg, The Netherlands)

  • S. L. van de Velde

    (University of Twente, Enschede, The Netherlands)

Abstract

We consider the single-machine problem of scheduling n jobs to minimize the sum of the deviations of the job completion times from a given small common due date. For this NP-hard problem, we develop a branch-and-bound algorithm based on Lagrangian lower and upper bounds that are found in O ( n log n ) time. We identify conditions under which the bounds concur; these conditions can be expected to be satisfied by many instances with n not too small. In our experiments with processing times drawn from a uniform distribution, the bounds concur for n ≥ 40. For the case where the bounds do not concur, we present a refined lower bound that is obtained by solving a subset-sum problem of small dimension to optimality. We further develop a 4/3-approximation algorithm based upon the Lagrangian upper bound.

Suggested Citation

  • J. A. Hoogeveen & H. Oosterhout & S. L. van de Velde, 1994. "New Lower and Upper Bounds for Scheduling Around a Small Common Due Date," Operations Research, INFORMS, vol. 42(1), pages 102-110, February.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:1:p:102-110
    DOI: 10.1287/opre.42.1.102
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    Citations

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    Cited by:

    1. 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.
    2. Sridharan, V. & Zhou, Z., 1996. "A decision theory based scheduling procedure for single-machine weighted earliness and tardiness problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 292-301, October.
    3. 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.
    4. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    5. Marjan van den Akker & Han Hoogeveen & Steef van de Velde, 2002. "Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 37-51, February.
    6. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    7. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.

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