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Cyclic Scheduling in a Stochastic Environment

Author

Listed:
  • Hongtao Zhang

    (The Hong Kong University of Science and Technology, Kowloon, Hong Kong)

  • Stephen C. Graves

    (The Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Cyclic or periodic schedules can be implemented in a job shop where demands for various products have a stable rate and mix. Numerous results on cyclic scheduling in deterministic settings are available, but studies considering uncertainties such as machine failure are rare. This paper examines the behavior of cyclic schedules in a stochastic environment characterized by random machine failures that may delay execution of tasks and thus may cause the actual production to deviate from a specified cyclic schedule. The authors intend to understand the behavior of cyclic schedules under uncertainty and to find those cyclic schedules that are the least disturbed by occurrences of machine failure. The cyclic scheduling problem of one or multiple machines can be formulated into a convex program for which the objective is to minimize a weighted sum of expected ergodic delays experienced by tasks. For one-machine schedules, the ergodic distributions of delays, as well as their expected values, are displayed. For multiple-machine schedules, a necessary condition for ergodicity is presented and stochastic lower bounds on task delays are derived.

Suggested Citation

  • Hongtao Zhang & Stephen C. Graves, 1997. "Cyclic Scheduling in a Stochastic Environment," Operations Research, INFORMS, vol. 45(6), pages 894-903, December.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:6:p:894-903
    DOI: 10.1287/opre.45.6.894
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    Citations

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    Cited by:

    1. Huynh, Candice H. & So, Kut C. & Gurnani, Haresh, 2016. "Managing a closed-loop supply system with random returns and a cyclic delivery schedule," European Journal of Operational Research, Elsevier, vol. 255(3), pages 787-796.
    2. Xiaoqiang Cai & Xianyi Wu & Xian Zhou, 2009. "Stochastic Scheduling Subject to Preemptive-Repeat Breakdowns with Incomplete Information," Operations Research, INFORMS, vol. 57(5), pages 1236-1249, October.
    3. 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.
    4. Scott Webster & Z. Kevin Weng, 2001. "Improving Repetitive Manufacturing Systems: Model and Insights," Operations Research, INFORMS, vol. 49(1), pages 99-106, February.

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