Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T15:42:03.988Z Has data issue: false hasContentIssue false

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
Affiliation:
Econometric Institute Erasmus University Rotterdam, The, Netherlands

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.

Type
Articles
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

REFERENCES

Rockafellar, R.T. & Wets, R.J. (1976). Nonanticipativity and L1martingales in stochastic optimization problems. Mathematical Programming Study 6: 170187;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: 559572.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: 661677.3.0.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: 4149.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: 317331.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: 597606.Google Scholar
Rinnooy, Kan A.H.G., Lageweg, B.J., & Lenstra, J.K. (1975). Minimizing total cost in one- machine scheduling. Operations Research 23: 908927.CrossRefGoogle Scholar
Botta, R.F. & Harris, C.M. (1986). Approximation with generalized hyperexponential distributions: Weak convergence results. Queueing Systems 2: 169190.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: 451456.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: 6169.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: 119126.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: 323333.CrossRefGoogle Scholar
Birge, J. & Glazebrook, K.D. (1988). Assessing the effects of machine breakdowns in stochasting scheduling. Operations Research Letters 6: 267271.Google Scholar
Glazebrook, K.D. (1987). Evaluating the effects of machine breakdowns in stochastic scheduling, Naval Research Logistical Quarterly 34: 319355.3.0.CO;2-5>CrossRefGoogle Scholar
Glazebrook, K.D. (1983). On stochastic scheduling problems with due dates. International Journal of Systems Science 14: 12591271.Google Scholar
Glazebrook, K.D. (1983). Methods for the evaluation of permutations as strategies in stochastic scheduling problems. Management Science 29: 11421155.Google Scholar
Glazebrook, K.D. (1976). Stochastic scheduling with order constraints. International Journal of Systems Science 7: 657666.CrossRefGoogle Scholar
Glazebrook, K.D. (1980). On single-machine sequencing with order constraints. Naval Research Logistical Quarterly 27: 123130.CrossRefGoogle Scholar
Glazebrook, K.D. (1980). On stochastic scheduling with precedence relations and switching costs. Journal of Applied Probability 17: 10161024.Google Scholar
Glazebrook, K.D. (1981). On non-preemptive strategies for stochastic scheduling problems in continuous time. International Journal of Systems Science 12: 771782.Google Scholar
Glazebrook, K.D. (1982). On the evaluation of fixed permutations as strategies in stochastic scheduling. Stochastic Processes and Their Applications 13: 171187.CrossRefGoogle Scholar
Glazebrook, K.D. & Gittins, J.C. (1981). On single machine scheduling with precedence relations and linear or discounted costs. Operations Research 29: 161173.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: 229251.CrossRefGoogle Scholar