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Journal of Optimization Theory and Applications

, Volume 1, Issue 3, pp 232–241 | Cite as

A problem in optimal stock management

  • Alain Y. Sprzeuzkouski
Contributed Papers

Abstract

We consider the planning of production over a prescribed period of time. More precisely, the problem is to minimize the cost integral (the time integral of the sum of the costs of production and storage) under the assumptions that the initial and final stocks are zero and that the production and the stock are nonnegative. Under this formulation, the problem can be considered as a Pontryagin-type problem with inequality constraints on the state variable and the control variable. We deduce from Pontryagin's maximum principle and Gamkrelidze's necessary conditions the existence and the uniqueness of an extremal trajectory.

Keywords

Control Variable Maximum Principle Inequality Constraint Stock Management Extremal Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Arrow, K. J., Karlin, S., andScarf, H.,Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, Stanford, California, 1958.Google Scholar
  2. 2.
    Barra, J. R., andBrodeau, M., Mimeographed Notes, Faculté des Sciences de Grenoble, 1964.Google Scholar
  3. 3.
    Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., andMishchenko, E. F.,The Mathematical Theory of Optimal Processes, John Wiley and Sons (Interscience Publishers), New York, 1962.Google Scholar
  4. 4.
    Leitmann, G.,An Introduction to Optimal Control, Chapter 4, McGraw-Hill Book Company, New York, 1966.Google Scholar

Copyright information

© Plenum Publishing Corporation 1967

Authors and Affiliations

  • Alain Y. Sprzeuzkouski
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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