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An optimal online algorithm for single machine scheduling to minimize total general completion time

Author

Listed:
  • Ming Liu

    (Tongji University
    Xi’an Jiaotong University)

  • Chengbin Chu

    (Ecole Centrale Paris)

  • Yinfeng Xu

    (Xi’an Jiaotong University)

  • Jiazhen Huo

    (Tongji University)

Abstract

We study the online problem of single machine scheduling to minimize total general completion time. General completion time is defined as $C^{\alpha}_{j}=(C_{j})^{\alpha}$ , where C j denotes the completion time of job J j and α≥1 is a constant integer. Total general completion time characterizes the feather in service that when a customer is served later in time, his dissatisfaction increases in a manner of power function. The objective function ∑(C j ) α can also be viewed as a total weighted completion time, but the “weight” is no longer a constant number. Our purpose to minimize customers’ total dissatisfaction. The problem is online in the sense that all jobs arrive over time. Each job’s processing time becomes known at its arrival time. Preemption is not allowed. For this online problem, we show that a lower bound on competitive ratio is 2 α and prove that D-SPT (delayed shortest processing time) algorithm is optimal with a competitive ratio 2 α .

Suggested Citation

  • Ming Liu & Chengbin Chu & Yinfeng Xu & Jiazhen Huo, 2012. "An optimal online algorithm for single machine scheduling to minimize total general completion time," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 189-195, February.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:2:d:10.1007_s10878-010-9348-0
    DOI: 10.1007/s10878-010-9348-0
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    Citations

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    Cited by:

    1. Gawiejnowicz, Stanisław & Kurc, Wiesław, 2015. "Structural properties of time-dependent scheduling problems with the lp norm objective," Omega, Elsevier, vol. 57(PB), pages 196-202.
    2. Xing Chai & Wenhua Li & Yuejuan Zhu, 2021. "Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine," Annals of Operations Research, Springer, vol. 298(1), pages 79-93, March.

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