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A diffusion model for the control of a dam

Published online by Cambridge University Press:  14 July 2016

J. A. Bather
J. A. Bather*
Affiliation:
University of Manchester
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Extract

A previous paper [2] was concerned with the determination of optimal policies for restocking an inventory which is continuously depleted by a random process of demands. The purpose of the present paper is to develop a similar model for controlling the output of a dam whose random input depends on a homogeneous Wiener process. This reversal of the roles of input and output does not, by itself, change the character of the problem. But the consideration of set-up costs for ordering replacements, which leads to inventory policies of the (s, S) type, has no counterpart here. It is natural to regard the dam as a device for smoothing out random fluctuations in a flow of water and, under utility assumptions which reflect this attitude, it follows that the optimal output rate is a continuous function of the level of water in the reservoir. Our main object is to determine this function.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 55 - 71
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Bather, J. A. (1962) Optimal regulation policies for finite dams. J. Soc. Indust. Appl. Math. 10, 395–423.CrossRefGoogle Scholar
[2] Bather, J. A. (1966) A continuous time inventory model. J. Appl. Prob. 3, 538–549 Google Scholar
[3] Doob, J. L. (1953) Stochastic Processes. John Wiley and Sons Inc., New York.Google Scholar
[4] Prabhu, N. U. (1965) Queues and Inventories. John Wiley and Sons Inc., New York.Google Scholar