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Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes

Author

Listed:
  • Xinrong Lu

    (Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China)

  • Zhaohui Liu

    (Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China)

Abstract

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M1 receives both low and high hierarchy jobs, while the second machine M2 only receives high hierarchy jobs. The machines have a speed ratio of s (s ≥ 1), and M2 runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.

Suggested Citation

  • Xinrong Lu & Zhaohui Liu, 2015. "Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-31.
  • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:05:n:s0217595915500323
    DOI: 10.1142/S0217595915500323
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    Cited by:

    1. Leung, Joseph Y.-T. & Li, Chung-Lun, 2016. "Scheduling with processing set restrictions: A literature update," International Journal of Production Economics, Elsevier, vol. 175(C), pages 1-11.
    2. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.

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