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On-line production order scheduling with preemption penalties

Author

Listed:
  • Feifeng Zheng

    (Xi’an JiaoTong University)

  • Yinfeng Xu

    (Xi’an JiaoTong University
    The State Key Lab for Manufacturing Systems Engineering)

  • E. Zhang

    (Shanghai University of Finance and Economics)

Abstract

This paper studies the on-line production order scheduling problem where each preemption causes a penalty, and the objective is to maximize the net profit, i.e., the total weights of completed orders minus the total penalties caused by preemptions. Two greedy strategies are shown to be at best $$O(\Delta^2)$$ and $$(4\Delta+2\Delta\sqrt{4+1/\Delta}+1)$$ -competitive respectively, where Δ is the ratio between the longest and shortest length of order. After that we mainly present an improved strategy, named WAL, which takes advantage of the knowledge of Δ and is proved to be $$\left(3\Delta + o(\Delta)\right)$$ -competitive for Δ > 9. Furthermore, two lower bounds for deterministic strategies, $$(1.366\Delta + 0.366)$$ and 6.33, are given for the cases of nonuniform and uniform length respectively.

Suggested Citation

  • Feifeng Zheng & Yinfeng Xu & E. Zhang, 2007. "On-line production order scheduling with preemption penalties," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 189-204, February.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:2:d:10.1007_s10878-006-9027-3
    DOI: 10.1007/s10878-006-9027-3
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    References listed on IDEAS

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    1. Tak-Wah Lam & Tusen-Wan Johnny Ngan & Kar-Keung To, 2005. "A Tighter Extra-Resource Analysis of Online Deadline Scheduling," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 157-165, March.
    2. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
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    Cited by:

    1. Nicholas G. Hall & Marc E. Posner & Chris N. Potts, 2021. "Online production planning to maximize the number of on-time orders," Annals of Operations Research, Springer, vol. 298(1), pages 249-269, March.

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