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Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Author

Listed:
  • I. Adiri
  • E. Frostig
  • A. H. G. Rinnooy Kan

Abstract

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.

Suggested Citation

  • I. Adiri & E. Frostig & A. H. G. Rinnooy Kan, 1991. "Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 261-271, April.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:2:p:261-271
    DOI: 10.1002/1520-6750(199104)38:23.0.CO;2-I
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    References listed on IDEAS

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    1. Michael Pinedo, 1983. "Stochastic Scheduling with Release Dates and Due Dates," Operations Research, INFORMS, vol. 31(3), pages 559-572, June.
    2. Hiroshi Kise & Toshihide Ibaraki & Hisashi Mine, 1978. "A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times," Operations Research, INFORMS, vol. 26(1), pages 121-126, February.
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    Cited by:

    1. Chen, Wen-Jinn, 2009. "Minimizing number of tardy jobs on a single machine subject to periodic maintenance," Omega, Elsevier, vol. 37(3), pages 591-599, June.
    2. Yarlin Kuo & Zi‐Ann Chang, 2007. "Integrated production scheduling and preventive maintenance planning for a single machine under a cumulative damage failure process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 602-614, September.
    3. 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.
    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. Xiaoqiang Cai & Xiaoqian Sun & Xian Zhou, 2004. "Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 800-817, September.
    6. W J Chen, 2006. "Minimizing total flow time in the single-machine scheduling problem with periodic maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 410-415, April.

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