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Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan

Author

Listed:
  • Xing Chai

    (Zhengzhou University)

  • Wenhua Li

    (Zhengzhou University
    Hennan Key Laboratory of Financial Engineering)

Abstract

We study the online scheduling problem on m identical parallel machines to minimize makespan, i.e., the maximum completion time of the jobs, where m is given in advance and the jobs arrive online over time. We assume that the jobs, which arrive at some nonnegative real times, are of equal-length and are restricted by chain precedence constraints. Moreover, the jobs arriving at distinct times are independent, and so, only the jobs arriving at a common time are restricted by the chain precedence constraints. In the literature, a best possible online algorithm of a competitive ratio 1.3028 is given for the case $$m=2$$ m = 2 . But the problem is unaddressed for $$m\ge 3$$ m ≥ 3 . In this paper, we present a best possible online algorithm for the problem with $$m\ge 3$$ m ≥ 3 , where the algorithm has a competitive ratio of 1.3028 for $$3\le m\le 5$$ 3 ≤ m ≤ 5 and 1.3146 for $$m\ge 6$$ m ≥ 6 .

Suggested Citation

  • Xing Chai & Wenhua Li, 2018. "Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 472-492, August.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-018-0309-3
    DOI: 10.1007/s10878-018-0309-3
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    References listed on IDEAS

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    1. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    2. Peter Brucker & Johann Hurink & Wieslaw Kubiak, 1999. "Scheduling identical jobs with chain precedence constraints on two uniform machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 211-219, April.
    3. Agnetis, Alessandro & Flamini, Marta & Nicosia, Gaia & Pacifici, Andrea, 2010. "Scheduling three chains on two parallel machines," European Journal of Operational Research, Elsevier, vol. 202(3), pages 669-674, May.
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    Cited by:

    1. Feifeng Zheng & Yuhong Chen & Ming Liu & Yinfeng Xu, 2022. "Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1060-1076, September.

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