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A Note on One-Machine Scheduling Problems with Imperfect Information

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 consider one-machine scheduling problems with or without a perfect machine and random processing times and derive among other results elimination criteria for different classes of cost functions.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 3 , July 1991 , pp. 317 - 331
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
Widder, D.V. (1971). An introduction to transform theory. New York: Academic Press.Google Scholar
Reuter, H. & Riedrich, T. (1981). On maximal Sets of functions compatible with a partial ordering for distribution functions. Mathemat. Operat.-Forschung Statist., Ser. Optimiz. 12: 597–606.Google Scholar
Roberts, A.W. & Varberg, D.E. (1973). Convex functions. New York: Academic Press.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.Google Scholar
Cox, D.R. (1970). Renewal theory. New York: Methuen & Co. Ltd.Google Scholar
Frenk, J.B.G. (1987). Renewal theory and completely monotone functions. Report 8759/A, Econometric Institute, Erasmus University, Rottrdam.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
Pinedo, M.L. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31: 559–572.Google Scholar
Rinnooy, Kan A.H.G., Lageweg, B.J. & Lenstra, J.K. (1975). Minimizing total cost in onemachine scheduling. Operations Research 23: 908–927.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.Google Scholar
French, S. (1982). Sequencing and scheduling. New York: Ellis Harwood Ltd.Google Scholar
Frenk, J.B.G. (1991). A general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering. Probability in the Engineering and Informational Sciences 5: 297–315.Google Scholar
Feller, W. (1970). An introduction to probability theory and its applications, Vol. 2. New York: Wiley.Google Scholar
Karlin, S. & Taylor, H.M. (1975). A first course in stochastic processes, 2nd ed.New York: Academic Press.Google Scholar
Brown, M. (1980). Bounds, inequalities, and monotonicity properties for some specialized renewal processes. Annals of Probability 8: 227–240.Google Scholar
Lawler, E. L. (1979). Efficient implementation of dynamic programming algorithms for sequencing problems. Report BW 106, Mathematical Centre, Amsterdam.Google Scholar
Rudin, W. (1982). Principles of mathematical analysis (international student edition), 3rd ed.Auckland, New Zealand: McGraw-Hill.Google Scholar