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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
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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.

Information

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

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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