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Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns

  • S.I. : CoDIT2017-Combinatorial Optimization
  • Published:
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Abstract

In this article, we discuss the optimal scheduling problem of the recently introduced model for partial loss due to machine breakdowns, which fills up a significant gap in the existing literature. More specifically, we consider the problem of processing a number of jobs with arbitrary random processing times by a machine subject to general stochastic breakdowns, where each breakdown may cause an uncertain loss of the work achieved on the job being processed. The objective is to maximize the expected weighted discounted reward of completing the jobs in the class of unrestricted dynamic policies. We obtain the optimal dynamic polices using multi-armed bandit process methodology, which are characterized by a set of Gittins indices as solutions to a system of integral equations. Optimal solutions for a number of problems with specific loss patterns are derived. Application of the theory to the classical no-loss model is also discussed which leads to new results.

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Notes

  1. When a job of higher priority arrives, the machine has to process it immediately, causing a disruption to the regular job being processed. For regular jobs, interruptions by jobs with higher priority are equivalent, in effect, to breakdowns of the machine.

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Acknowledgements

This research is partially supported by: (1) Natural Science Foundation of China (Nos. 71531003, 71432004), Research Grants Council of Hong Kong (No. T32-102/14), the Leading Talent Program of Guangdong Province (No. 2016LJ06D703), and Shenzhen Science and Technology Innovation Committee (Grant No. ZDSYS20170725140921348) to Xiaoqiang Cai; (2) Natural Science Foundation of China (Nos. 71371074, 71771089) to Xianyi Wu.

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Authors and Affiliations

  1. Shenzhen Key Laboratory of IoT Intelligent Systems and Wireless Network Technology, The Chinese University of Hong Kong, Shenzhen, People’s Republic of China

    Xiaoqiang Cai

  2. The Shenzhen Research Institute of Big Data, Guangdong, People’s Republic of China

    Xiaoqiang Cai

  3. Department of Statistics and Actuarial Science, East China Normal University, Shanghai, People’s Republic of China

    Xianyi Wu

  4. Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia

    Xian Zhou

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  1. Xiaoqiang Cai
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Correspondence to Xiaoqiang Cai.

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Cai, X., Wu, X. & Zhou, X. Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns. Ann Oper Res 298, 43–64 (2021). https://doi.org/10.1007/s10479-018-2962-4

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