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Two Approximation Schemes For Scheduling On Parallel Machines Under A Grade Of Service Provision

Author

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  • WEIDONG LI

    (Department of Atmospheric Science, Yunnan University, Kunming 650091, P. R. China)

  • JIANPING LI

    (Department of Mathematics, Yunnan University, Kunming 650091, P. R. China)

  • TONGQUAN ZHANG

    (School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming 650031, P. R. China)

Abstract

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

Suggested Citation

  • Weidong Li & Jianping Li & Tongquan Zhang, 2012. "Two Approximation Schemes For Scheduling On Parallel Machines Under A Grade Of Service Provision," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-12.
    • Handle: RePEc:wsi:apjorx:v:29:y:2012:i:05:n:s0217595912500297
    DOI: 10.1142/S0217595912500297
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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. Xiaofei Liu & Man Xiao & Weidong Li & Yaoyu Zhu & Lei Ma, 2023. "Algorithms for single machine scheduling problem with release dates and submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.

    More about this item

    Keywords

    Makespan; EPTAS; FPTAS;
    All these keywords.

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