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A General Framework for Stochastic One-machine Scheduling Problems with Zero Release Times and No Partial Ordering

Published online by Cambridge University Press:  27 July 2009

J. B. G. frenk
J. B. G. frenk
Affiliation:
Econometric Institute Erasmus University Rotterdam, The, Netherlands
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Abstract

In this paper we present a general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering and review and extend some of the results for nonpreemptive permutation schedules recently obtained for these models.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 3 , July 1991 , pp. 297 - 315
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Rockafellar, R.T. & Wets, R.J. (1976). Nonanticipativity and L1martingales in stochastic optimization problems. Mathematical Programming Study 6: 170–187;CrossRefGoogle Scholar
also in Wets, R.J. (ed.), Stochastic systems: Modelling, identification and optimization. Amsterdam: North-Holland.Google Scholar
Pinedo, M.L. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31: 559–572.CrossRefGoogle 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
French, S. (1982). Sequencing and scheduling. New York: Ellis Horwood Ltd.Google Scholar
Pinedo, M.L. & 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.Google Scholar
Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
Frenk, J.B.G. (1991). A note on one-machine scheduling problems with imperfect information. Probability in the Engineering and Informational Sciences 5: 317–331.Google Scholar
Reuter, H. & Riedrich, T. (1981). On maximal sets of functions compatible with a partial or-dering for distribution functions. Mathemat. Operat.-Forschung Statist. Ser. Optimiz. 12: 597–606.Google Scholar
Rinnooy, Kan A.H.G., Lageweg, B.J., & Lenstra, J.K. (1975). Minimizing total cost in one- machine scheduling. Operations Research 23: 908–927.CrossRefGoogle Scholar
Botta, R.F. & Harris, C.M. (1986). Approximation with generalized hyperexponential distributions: Weak convergence results. Queueing Systems 2: 169–190.Google Scholar
Rothkopf, M.H. & Smith, S.A. (1984). There are no undiscovered priority index sequencing rules for minimizing total delay costs. Operations Research 32: 451–456.Google Scholar
Roberts, A.W. & Varberg, D.E. (1973). Convex functions. New York: Academic Press.Google Scholar
Lawler, E.L. (1979). Efficient implementation of dynamic programming algorithmsfor sequencing problems. Report BW 106, Mathematical Centre, Amsterdam.Google Scholar
Patel, J.K., Kapadia, C.H., & Owen, D.B. (1976). Handbook of statistical distributions. New York: Marcel Dekker Inc.Google Scholar
Ross, S.M. (1985). Introduction to probability models. New York: Academic Press.Google Scholar
Pinedo, M.L. & Wie, S. (1986). Inequalities for stochastic flow shops and job shops. Applied Stochastic Models and Data Analysis 2: 61–69.CrossRefGoogle Scholar
Draisma, G. & Frenk, J.B.G. (1991). Computational results for stochastic single-machine scheduling problems (to appear).Google Scholar
Boxma, O.J. & Forst, F.G. (1986). Minimizing the expected weighted number of tardy jobs in stochastic flow shops. Operations Research Letters 5: 119–126.CrossRefGoogle Scholar
Righter, R. & Shanthikumar, J.G. (1989). Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Probability in the Engineering and Informational Sciences 3: 323–333.CrossRefGoogle Scholar
Birge, J. & Glazebrook, K.D. (1988). Assessing the effects of machine breakdowns in stochasting scheduling. Operations Research Letters 6: 267–271.Google Scholar
Glazebrook, K.D. (1987). Evaluating the effects of machine breakdowns in stochastic scheduling, Naval Research Logistical Quarterly 34: 319–355.3.0.CO;2-5>CrossRefGoogle Scholar
Glazebrook, K.D. (1983). On stochastic scheduling problems with due dates. International Journal of Systems Science 14: 1259–1271.Google Scholar
Glazebrook, K.D. (1983). Methods for the evaluation of permutations as strategies in stochastic scheduling problems. Management Science 29: 1142–1155.Google Scholar
Glazebrook, K.D. (1976). Stochastic scheduling with order constraints. International Journal of Systems Science 7: 657–666.CrossRefGoogle Scholar
Glazebrook, K.D. (1980). On single-machine sequencing with order constraints. Naval Research Logistical Quarterly 27: 123–130.CrossRefGoogle Scholar
Glazebrook, K.D. (1980). On stochastic scheduling with precedence relations and switching costs. Journal of Applied Probability 17: 1016–1024.Google Scholar
Glazebrook, K.D. (1981). On non-preemptive strategies for stochastic scheduling problems in continuous time. International Journal of Systems Science 12: 771–782.Google Scholar
Glazebrook, K.D. (1982). On the evaluation of fixed permutations as strategies in stochastic scheduling. Stochastic Processes and Their Applications 13: 171–187.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
Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
Eijgermans, P.L.M. (1988). Een-machine volgorde problemen met imperfecte informatie. Masters thesis, Erasmus University, Rotterdam (in Dutch).Google Scholar
Fisher, M.L. (1976). A dual algorithm for the one-machine scheduling problem. Mat hematical Programming 11: 229–251.CrossRefGoogle Scholar