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Characterization of the optimal class of output policies in a control model of a finite dam

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University of Jerusalem
*
∗Postal address: The Jerusalem School of Business Administration, The Hebrew University of Jerusalem, Jerusalem, Israel.
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Abstract

In this paper we characterize the optimal class of output policies in a control model of a dam having a finite capacity. The input of water into the dam is determined by a Wiener process with positive drift. Water may be released at either of two possible rates 0 or M. At any time the output rate can be increased from 0 to M with a cost of K, (K ≧ 0) or decreased from M to 0 with zero cost, any such changes taking effect instantaneously. There is a reward of A monetary units for each unit of output, (A ≧ 0). The problem is to formulate an optimal output policy which maximizes the long-run average net reward per unit time.

Keywords

WIENER PROCESSSTATIONARY POLICYCONTROLSWITCHING COSTHITTING TIMESAMPLE PATHSTRONG MARKOV PROPERTY
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 913 - 923
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Research carried out while the author was at Northwestern University.

References

[1] Faddy, M. J. (1974) Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob. 11, 111–121.CrossRefGoogle Scholar
[2] Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[3] Zuckerman, D. (1977) Two-stage output procedure of a finite dam. J. Appl. Prob. 14, 421–425.Google Scholar
[4] Zuckerman, D. (1979) N-stage output procedure of a finite dam. Z. Operat. Res. 23, 179–187.Google Scholar