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A Dynamic Programming Algorithm for Embedded Markov Chains when the Planning Horizon is at Infinity

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  • John S. de Cani

    (U.S. Naval Air Development Center and University of Pennsylvania)

Abstract

This paper presents an algorithm for the solution of dynamic programming problems requiring the determination of optimal policies for the control of a special class of stochastic processes when the time horizon of the planning period is at infinity. These processes can be mathematically described as discrete time parameter Markov chains with a finite number of states which have been "embedded" in continuous time in the sense that the time between transitions is a random variable whose probability distribution depends only on the states between which the transition takes place. Such processes are called Markov-renewal processes. The Markov processes considered by R. A. Howard in [1] are really two special cases of this somewhat wider class of stochastic processes. In these two special cases, the algorithm of this paper is identical with Howard's. In fact, with only slight modification, Howard's algorithm can be extended to this wider class of stochastic processes.

Suggested Citation

  • John S. de Cani, 1964. "A Dynamic Programming Algorithm for Embedded Markov Chains when the Planning Horizon is at Infinity," Management Science, INFORMS, vol. 10(4), pages 716-733, July.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:4:p:716-733
    DOI: 10.1287/mnsc.10.4.716
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    Cited by:

    1. Nooshin Salari & Viliam Makis, 2020. "Application of Markov renewal theory and semi‐Markov decision processes in maintenance modeling and optimization of multi‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 548-558, October.

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