Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-21T12:18:50.229Z Has data issue: false hasContentIssue false
  • English
  • Français

On Nonpreemptive Policies for Stochastic Single-Machine Scheduling with Breakdowns

Published online by Cambridge University Press:  27 July 2009

Kevin D. Glazebrook
Kevin D. Glazebrook
Affiliation:
Department of Mathematics and Statistics University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A set of stochastic jobs is to be processed on a single machine that is subject to breakdown. All jobs make progress as they are processed in the absence of machine breakdowns. However, breakdowns cause setbacks to (possibly) all jobs in the system, except those that have already been completed. With machines subject only to fairly mild restrictions on this “damage” process, we demonstrate the existence of a nonpreemptive policy that is optimal in the class of all preemptive ones.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 77 - 87
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.Google Scholar
Birge, J., Frenk, J.B.G., Mittenthal, J., & Rinnooy, Kan A.H.G. (1990). Single machine scheduling subject to stochastic breakdowns. Naval Research Logistics 37: 661–677.3.0.CO;2-3>CrossRefGoogle Scholar
Gittins, J.C. (1979). Bandit processes and dynamic allocation indices (with discussion). Journal of the Royal Statistical Society B41: 148–164.Google Scholar
Glazebrook, K.D. (1981). On non-preemptive strategies in stochastic scheduling. Naval Research Logistics Quarterly 28: 289–300.CrossRefGoogle Scholar
Glazebrook, K.D. (1983). Methods for the evaluation of permutations as strategies in stochastic scheduling. Management Science 29: 1142–1155.CrossRefGoogle Scholar
Glazebrook, K.D. (1984). Scheduling stochastic jobs on a single machine subject to breakdowns. Naval Research Logistics Quarterly 31: 251–264.CrossRefGoogle Scholar
Glazebrook, K.D. (1987). Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval Research Logistics Quarterly 34: 319–335.3.0.CO;2-5>CrossRefGoogle Scholar
Glazebrook, K.D. & Gittins, J.C. (1981). On single-machine scheduling with precedence relations and linear or discounted costs. Operations Research 29: 161–173.CrossRefGoogle Scholar
Meilijson, I. & Weiss, G. (1977). Multiple feedback at a single server station. Stochastic Processes Applications 5: 195–205.CrossRefGoogle Scholar
Nash, P. & Gittins, J.C. (1977). A Hamiltonian approach to optimal stochastic resource allocation. Advances in Applied Probability 9: 55–68.CrossRefGoogle Scholar
Pinedo, M. & Rammouz, E. (1988). A note on stochastic scheduling on a single machine subject to breakdown and repair. Probability in the Engineering and Informational Sciences 2: 41–49.CrossRefGoogle Scholar
Righter, R. & Shanthikumar, J.G. (1989). Scheduling multiclass single server queueing systems to stochastically maximise the number of successful departures. Probability in the Engineering and Informational Sciences 3: 323–333.CrossRefGoogle Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco: Holden-Day.Google Scholar
Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
Whittle, P. (1980). Multi-armed bandits and the Gittins' index. Journal of the Royal Statistical Society B42: 143–149.Google Scholar