Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-08T05:29:14.470Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Stochastic Scheduling on a Single Machine Subject to Breakdown and Repair

Published online by Cambridge University Press:  27 July 2009

Michael Pinedo  and
Elias Rammouz
Michael Pinedo
Affiliation:
Department ofIndustrial Engineering and Operations Research Columbia University New York, New York 10027
Elias Rammouz
Affiliation:
Department ofIndustrial Engineering and Operations Research Columbia University New York, New York 10027
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a single machine and n jobs. The machine is subject to breakdown and repair. Job j has a weight wj, a random processing time Xj, and is available for processing from a random time Rj on. The jobs may be subject to precedence constraints. We are interested in optimal policies that minimize the following objective functions: (i) the weighted sum of the completion times; (ii) the weighted sum of an exponential function of the completion times; and (iii) the weighted number of late jobs having due dates.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 41 - 49
Copyright
Copyright © Cambridge University Press 1988

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

Banerjee, B.P. (1965). Single-facility sequencing with random execution times. Operations Research 13: 358–364.CrossRefGoogle Scholar
Birge, J., Mittenthal, J., Rinnooy, Kan A.H.G. & Frenk, M. (1986). Single-machine scheduling subject to stochastic breakdowns. Erasmus University, Rotterdam.Google Scholar
Blau, R.A. (1973). N-job, one machine sequencing problems under uncertainty. Management Science 20: 101–109.CrossRefGoogle Scholar
Bruno, J. & Hofri, M. (1975). On scheduling chains of jobs on one processor with limited preemptions. SIAM Journal of Computing 4: 478–490.CrossRefGoogle Scholar
Derman, C., Lieberman, G. & Ross, S.M. (1978). A renewal decision problem. Management Science 24: 554–561.Google Scholar
Gittins, J.C. (1979). Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society, Series B, 41: 148–177.Google Scholar
Gittins, J.C. & Glazebrook, K.D. (1981). On single machine scheduling with precedence relations and linear or discounted costs. Operations Research 29: 161–173.Google Scholar
Glazebrook, K.D. (1981). On nonpreemptive strategies in stochastic scheduling. Naval Research Logistics Quarterly 28: 289–300.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: 319–336.3.0.CO;2-5>CrossRefGoogle Scholar
Kelly, F.P. (1979). Reversibility and stochastic networks. New York: John Wiley and Sons.Google Scholar
Lawler, E.L. (1978). Sequencing jobs to optimize total weighted completion time subject to precedence constraints. Annals of Discrete Mathematics 2: 75–90.CrossRefGoogle Scholar
Meilijson, I. & Weiss, G. (1977). Multiple feedback at a single-server station. Stochastic processes and their application 5: 195–205.CrossRefGoogle Scholar
Monma, C. & Sidney, J. (1979). Sequencing with series—parallel precedence constraints. Mathematics of Operations Research 4: 215–224.CrossRefGoogle Scholar
Pinedo, M.L. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31: 559–572.CrossRefGoogle Scholar
Sevcik, K.C. (1972). The use of service-time distributions in scheduling. Technical Report CSRG-14, University of Toronto.Google Scholar