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Scheduling jobs that are subject to failure propagation

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  • Sid Browne
  • Kevin D. Glazebrook

Abstract

A single machine is available to process a collection of stochastic tasks. Processing is interrupted when the machine breaks down. We introduce a new model of breakdowns that more realistically incorporates the effects that job processing may have on the machine. This failure propagation model is equivalent to a Bayesian formulation in which learning about breakdown rates occurs as jobs evolve. Optimal scheduling policies are described in terms of Gittins indices and these indices are characterised in two special cases. For example, we obtain conditions which ensure that an optimal policy will only preempt a job's processing either at its completion or at a machine breakdown. We also bound the value lost by simplistic modelling which ignores the learning phenomenon. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:2:p:265-288
    DOI: 10.1002/(SICI)1520-6750(199603)43:23.0.CO;2-8
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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