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Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs

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  • Xiaoqiang Cai

    (The Chinese University of Hong Kong, Shatin, Hong Kong)

  • Sean Zhou

    (The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Abstract

This paper addresses a stochastic scheduling problem in which a set of independent jobs are to be processed by a number of identical parallel machines under a common deadline. Each job has a processing time, which is a random variable with an arbitrary distribution. Each machine is subject to stochastic breakdowns, which are characterized by a Poisson process. The deadline is an exponentially distributed random variable. The objective is to minimize the expected costs for earliness and tardiness, where the cost for an early job is a general function of its earliness while the cost for a tardy job is a fixed charge. Optimal policies are derived for cases where there is only a single machine or are multiple machines, the decision-maker can take a static policy or a dynamic policy, and job preemptions are allowed or forbidden. In contrast to their deterministic counterparts, which have been known to be NP-hard and are thus intractable from a computational point of view, we find that optimal solutions for many cases of the stochastic problem can be constructed analytically.

Suggested Citation

  • Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:3:p:422-437
    DOI: 10.1287/opre.47.3.422
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    References listed on IDEAS

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    4. Xiaoqiang Cai & Xianyi Wu & Xian Zhou, 2021. "Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns," Annals of Operations Research, Springer, vol. 298(1), pages 43-64, March.
    5. Wan, Guohua & Yen, Benjamin P.-C., 2009. "Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 195(1), pages 89-97, May.
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    7. Alcaide, D. & Rodriguez-Gonzalez, A. & Sicilia, J., 2002. "An approach to solve the minimum expected makespan flow-shop problem subject to breakdowns," European Journal of Operational Research, Elsevier, vol. 140(2), pages 384-398, July.
    8. Sam Ransbotham & Ishwar Murthy & Sabyasachi Mitra & Sridhar Narasimhan, 2011. "Sequential Grid Computing: Models and Computational Experiments," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 174-188, May.

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