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Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan

Author

Listed:
  • Jinwei Gu

    (Shanghai University of Electric Power)

  • Manzhan Gu

    (Shanghai University of Finance and Economics)

  • Xiwen Lu

    (East China University of Science and Technology)

  • Ying Zhang

    (Georgia Institute of Technology)

Abstract

This paper studies the large-scale stochastic job shop scheduling problem with general number of similar jobs, where the processing times of the same step are independently drawn from a known probability distribution, and the objective is to minimize the makespan. For the stochastic problem, we introduce the fluid relaxation of its deterministic counterpart, and define a fluid schedule for the fluid relaxation. By tracking the fluid schedule, a policy is proposed for the stochastic job shop scheduling problem. The expected value of the gap between the solution produced by the policy and the optimal solution is proved to be O(1), which indicates the policy is asymptotically optimal in expectation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0294-6
    DOI: 10.1007/s10878-018-0294-6
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    References listed on IDEAS

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    1. 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.
    2. Penn, Michal & Raviv, Tal, 2009. "An algorithm for the maximum revenue jobshop problem," European Journal of Operational Research, Elsevier, vol. 193(2), pages 437-450, March.
    3. J. G. Dai & Gideon Weiss, 2002. "A Fluid Heuristic for Minimizing Makespan in Job Shops," Operations Research, INFORMS, vol. 50(4), pages 692-707, August.
    4. Dimitris Bertsimas & David Gamarnik & Jay Sethuraman, 2003. "From Fluid Relaxations to Practical Algorithms for High-Multiplicity Job-Shop Scheduling: The Holding Cost Objective," Operations Research, INFORMS, vol. 51(5), pages 798-813, October.
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    Cited by:

    1. Dalila B. M. M. Fontes & S. Mahdi Homayouni & Mauricio G. C. Resende, 2022. "Job-shop scheduling-joint consideration of production, transport, and storage/retrieval systems," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1284-1322, September.

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