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Single‐machine scheduling of stochastic jobs subject to deterioration or delay

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  • K. D. Glazebrook

Abstract

N jobs are available for processing by a single machine. Jobs make (stochastic) progress while being processed but deteriorate while awaiting processing. The pioneering work of Browne and Yechiali, who developed scheduling policies for such models, is extended (i) to incorporate a precedence relation on the job set, delimiting the class of admissible policies, and (ii) to preemptive scheduling models. For the latter, we demonstrate that under appropriate conditions there is an optimal policy which is nonpreemptive. This is also achieved for a class of preemptive models in which processing generates delays for waiting jobs. A single class of algorithms is shown to generate optimal policies for many of the problems considered. © 1992 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:5:p:613-633
    DOI: 10.1002/1520-6750(199208)39:53.0.CO;2-P
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    References listed on IDEAS

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    1. 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.
    2. Michael L. Pinedo & Sheldon M. Ross, 1980. "Scheduling Jobs Subject to Nonhomogeneous Poisson Shocks," Management Science, INFORMS, vol. 26(12), pages 1250-1257, December.
    3. 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.
    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. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    6. 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.
    7. 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.
    8. K. D. Glazebrook, 1980. "On single‐machine sequencing with order constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 123-130, March.
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    Cited by:

    1. T.C. Edwin Cheng & Qing Ding & Mikhail Y. Kovalyov & Aleksander Bachman & Adam Janiak, 2003. "Scheduling jobs with piecewise linear decreasing processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 531-554, September.
    2. K.D. Glazebrook & H.M. Mitchell, 2002. "An index policy for a stochastic scheduling model with improving/deteriorating jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 706-721, October.
    3. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.

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