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Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time

Author

Listed:
  • Xing Chai

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

  • Lingfa Lu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

  • Wenhua Li

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

  • Liqi Zhang

    (College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan 450003, P. R. China)

Abstract

In this paper, we consider the online single machine scheduling problem to minimize the maximum weighted completion time of the jobs. For the preemptive problem, we show that the LW (Largest Weight first) rule yields an optimal schedule. For the non-preemptive problem, Li [Li, W (2015). A best possible online algorithm for the parallel-machine scheduling to minimize the maximum weighted completion time. Asia-Pacific Journal of Operational Research, 32(4), 1550030 (10 pages)] presented a lower bound 2, and then provided an online algorithm with a competitive ratio of 3. In this paper, we present two online algorithms with the best-possible competitive ratio of 2 for the non-preemptive problem.

Suggested Citation

  • Xing Chai & Lingfa Lu & Wenhua Li & Liqi Zhang, 2018. "Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-11, December.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:06:n:s0217595918500483
    DOI: 10.1142/S0217595918500483
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    References listed on IDEAS

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    1. Edward J. Anderson & Chris N. Potts, 2004. "Online Scheduling of a Single Machine to Minimize Total Weighted Completion Time," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 686-697, August.
    2. Wenjie Li, 2015. "A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-10.
    3. Nong, Q.Q. & Cheng, T.C.E. & Ng, C.T., 2011. "Two-agent scheduling to minimize the total cost," European Journal of Operational Research, Elsevier, vol. 215(1), pages 39-44, November.
    4. Gouchuan Zhang & Xiaoqiang Cai & C.K. Wong, 2001. "On‐line algorithms for minimizing makespan on batch processing machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 241-258, April.
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    Cited by:

    1. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.

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