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Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines

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  • Manzhan Gu
  • Xiwen Lu

Abstract

We study the stochastic online scheduling on m uniform machines with the objective to minimize the expected value of total weighted completion times of a set of jobs that arrive over time. For each job, the processing time is a random variable, and the distribution of processing time is unknown in advance. The actual processing time could be known only when the job is completed. For the problem, we propose a policy which is proved to be asymptotically optimal when the processing times and weights are uniformly bounded, i.e. the relative error of the solution achieved by our policy approaches zero as the number of jobs increases to infinity. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Manzhan Gu & Xiwen Lu, 2011. "Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines," Annals of Operations Research, Springer, vol. 191(1), pages 97-113, November.
    • Handle: RePEc:spr:annopr:v:191:y:2011:i:1:p:97-113:10.1007/s10479-011-0985-1
    DOI: 10.1007/s10479-011-0985-1
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    References listed on IDEAS

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    1. Mabel C. Chou & Hui Liu & Maurice Queyranne & David Simchi-Levi, 2006. "On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions," Operations Research, INFORMS, vol. 54(3), pages 464-474, June.
    2. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.
    3. Hui Liu & Maurice Queyranne & David Simchi‐Levi, 2005. "On the asymptotic optimality of algorithms for the flow shop problem with release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 232-242, April.
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    Cited by:

    1. Manzhan Gu & Xiwen Lu & Jinwei Gu, 2017. "An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 473-495, February.
    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.
    3. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 2022. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1796-1811, October.
    4. Jinwei Gu & Manzhan Gu & Xiwen Lu & Ying Zhang, 2018. "Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 142-161, July.
    5. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 0. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.

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