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Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time

Author

Listed:
  • Wenjie Li

    (School of Mathematical Sciences, Luoyang Normal University, Luoyang 471934, Henan, P. R. China)

  • Hailing Liu

    (College of Science, Henan Institute of Engineering, Zhengzhou 451191, Henan, P. R. China)

  • Shisheng Li

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, P. R. China)

Abstract

This paper studies online scheduling on m identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When m = 1, we prove that WSPT is an optimal online algorithm. When m ≥ 2, we first present a lower bound m2−2+m4 −4m+4 2m(m−1), and then show that WSPT is a 2-competitive online algorithm for the case m = 2. For the case in which m = 2 and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of 1+3 2.

Suggested Citation

  • Wenjie Li & Hailing Liu & Shisheng Li, 2018. "Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-12, August.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:04:n:s0217595918500240
    DOI: 10.1142/S0217595918500240
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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. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    3. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, August.
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