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

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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.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11201282 and 61304209), Humanity and Social Science Foundation of Ministry of Education of China (Grant No. 17YJAZH024).

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Authors and Affiliations

  1. College of Economics and Management, Shanghai University of Electric Power, Shanghai, 200090, China

    Jinwei Gu

  2. Institute of Scientific Computation and Financial Data Analysis, School of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Manzhan Gu

  3. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Xiwen Lu

  4. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ying Zhang

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  1. Jinwei Gu
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  2. Manzhan Gu
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  3. Xiwen Lu
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  4. Ying Zhang
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Correspondence to Manzhan Gu.

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Gu, J., Gu, M., Lu, X. et al. Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan. J Comb Optim 36, 142–161 (2018). https://doi.org/10.1007/s10878-018-0294-6

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  • DOI: https://doi.org/10.1007/s10878-018-0294-6

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