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Evaluating the effects of machine breakdowns in stochastic scheduling problems

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  • Kevin D. Glazebrook

Abstract

In most of the stochastic resource‐allocation problems discussed in the literature it is supposed that the key resource, herein called the machine, is continuously available until all tasks are completed. Plainly, this will often be an unrealistic assumption. This paper supposes that intermittent availability of the machine is due to a breakdown proces, and describes various approaches to the evaluation of the effect of breakdowns. Firstly, for the case of geometric up times, conditions are given under which breakdowns have no effect on optimal allocation strategies. Secondly, two different procedures are given which yield an upper bound on the loss incurred when a processing strategy is adopted under the assumption of no breakdowns, when in fact breakdowns do occur. The first of these is based on Gittins's indices and is described for the case of geometric up times, and the second uses a bounding argument on the breakdown process.

Suggested Citation

  • Kevin D. Glazebrook, 1987. "Evaluating the effects of machine breakdowns in stochastic scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 319-335, June.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:3:p:319-335
    DOI: 10.1002/1520-6750(198706)34:33.0.CO;2-5
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    References listed on IDEAS

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    1. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    2. K. D. Glazebrook, 1984. "Scheduling stochastic jobs on a single machine subject to breakdowns," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 251-264, June.
    3. K. D. Glazebrook & J. C. Gittins, 1981. "On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs," Operations Research, INFORMS, vol. 29(1), pages 161-173, February.
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    1. 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.
    2. Sid Browne & Kevin D. Glazebrook, 1996. "Scheduling jobs that are subject to failure propagation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 265-288, March.
    3. K. D. Glazebrook, 1992. "Single‐machine scheduling of stochastic jobs subject to deterioration or delay," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 613-633, August.
    4. J. Birge & J. B. G. Frenk & J. Mittenthal & A. H. G. Rinnooy Kan, 1990. "Single‐machine scheduling subject to stochastic breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 661-677, October.
    5. Lee, Chung-Yee & Lin, Chen-Sin, 2001. "Single-machine scheduling with maintenance and repair rate-modifying activities," European Journal of Operational Research, Elsevier, vol. 135(3), pages 493-513, December.
    6. Li, Wei & Glazebrook, Kevin D., 1998. "On stochastic machine scheduling with general distributional assumptions," European Journal of Operational Research, Elsevier, vol. 105(3), pages 525-536, March.
    7. Charles Du & Michael Pinedo, 1995. "A note on minimizing the expected makespan in flowshops subject to breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1251-1262, December.
    8. S. E. Pilnick & K. D. Glazebrook & D. P. Gaver, 1991. "Optimal sequential replenishment of ships during combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 637-668, October.

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