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N-Stage output procedure of a finite dam

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Summary

We examine the problem of optimizing operation of a reservoir with a finite capacity, described by the following model: The input of water into the reservoir is a Wiener process with positive drift. Water may be released at one ofR possible rates. At any time the output rate may be increased with costK per unit increase or it may be decreased to zero with zero cost. There is a reward ofA monetary units for each unit of output. The problem is to control the output in such a way as to maximize the long run average profit per unit time.

Zusammenfassung

In diesem Beitrag geht es um eine optimale Steuerung eines Wasserspeichers mit endlicher Kapazität: Der Zufluß wird durch einen Wiener Prozeß mit positivem Drift beschrieben. Der Abfluß erfolgt in einer von mehreren vorgegebenen Geschwindigkeitsstufen, die jedoch in jedem Zeitpunkt geändert werden kann. Eine Erhöhung der Abflußgeschwindigkeit ist im Gegensatz zu einer Verminderung mit Kosten verbunden. Die Abflußmengen führen zu pro Mengeneinheit konstanten Erlösen. Das Entscheidungsproblem besteht darin, eine Steuerung des Abflusses zu finden, die den durchschnittlichen Gewinn pro Zeiteinheit maximiert.

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References

  • Bather, J.: A diffusion model for the control of a dam. J. Appl. Prob.5, 1968, 55–71.

    Google Scholar 

  • Faddy, M.J.: Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob.11, 1974, 111–121.

    Google Scholar 

  • Feller, W.: An Introduction to Probability Theory and its Applications II. New York 1971.

  • Gessford, J., andS. Karlin: Optimal policy for hydroelectric operation. Studies in the Mathematical Theory of Inventory and Production. Ed. by K.J. Arrow, S. Karlin and H. Scarf. Stanford, California 1958, 179–200.

  • Haslett, J.: The control of a multipurpose reservoir. Adv. Appl. Prob.8, 1976, 592–609.

    Google Scholar 

  • Ito, K., andH.P. Mckean: Diffusion Processes and their Sample Paths. New York 1974.

  • Karlin, S., andH.M. Taylor: A First Course in Stochastic Processes. New York 1975.

  • Pliska, S.R.: A diffusion process model for the optimal operation of a reservoir system. J. Appl. Prob.12, 1975, 859–863.

    Google Scholar 

  • Russel, C.B.: An optimal policy for operating a multipurpose reservoir. Oper. Res.20, 1972, 1181–1189.

    Google Scholar 

  • Taylor, H.M.: A stopped Brownian motion formula. Ann. Prob.3, 1975, 234–246.

    Google Scholar 

  • Zuckerman, D.: Two-stage output procedure of a finite dam. J. Appl. Prob.14, 1977, 421–425.

    Google Scholar 

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Zuckerman, D. N-Stage output procedure of a finite dam. Zeitschrift für Operations Research 23, 179–187 (1979). https://doi.org/10.1007/BF01919482

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  • DOI: https://doi.org/10.1007/BF01919482

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