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Dynamically optimized replacement with a Markovian renewal process

Published online by Cambridge University Press:  14 July 2016

Johannes Siedersleben
Johannes Siedersleben*
Affiliation:
Universität Karlsruhe
*
∗ Postal address: Institut für Wirtschaftstheorie und Operations Research der Universität Karlsruhe, Kaiserstraße 12, Kollegium am Schloss, Bau IV, 7500 Karlsruhe 1, W. Germany.
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Abstract

We consider a system that gradually deteriorates. At random times Tn the system is inspected and may or may not be replaced, but it must be if its state is too bad. The process of deterioration is described by a Markovian renewal process. Under some monotonicity conditions we derive a policy for the finite and the infinite horizon which minimizes the total discounted costs. This paper is a generalization of a result of Feldman (1977).

Keywords

OPTIMAL REPLACEMENTMARKOV RENEWAL THEORYDYNAMIC PROGRAMMING

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 641 - 651
Copyright
Copyright © Applied Probability Trust 

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References

Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Denardo, E. V. (1967) Contraction mappings in the theory underlying dynamic programming. SIAM Rev. 9, 165–177.Google Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
Feldman, R. M. (1977) Optimal replacement with semi-Markov shock models using discounted costs. Maths. Operat. Res. 2, 78–90.Google Scholar
Nakagawa, T. (1976) On a replacement problem of a cumulative damage model. Operat. Res. Quart. 27, 895–900.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden Day, San Francisco.Google Scholar