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Countable-State, Continuous-Time Dynamic Programming with Structure

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  • Steven A. Lippman

    (University of California, Los Angeles, California)

Abstract

We consider the problem P of maximizing the expected discounted reward earned in a continuous-time Markov decision process with countable state and finite action space. (The reward rate is merely bounded by a polynomial.) By examining a sequence 〈 p N 〉 of approximating problems, each of which is a semi-Markov decision process with exponential transition rate Λ N , Λ N ↗ ∞, we are able to show that P is obtained as the limit of the P N . The value in representing P as the limit of P N is that structural properties present in each P N persist, in both the finite and the infinite horizon problem. Three queuing optimization models illustrating the method are given.

Suggested Citation

  • Steven A. Lippman, 1976. "Countable-State, Continuous-Time Dynamic Programming with Structure," Operations Research, INFORMS, vol. 24(3), pages 477-490, June.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:3:p:477-490
    DOI: 10.1287/opre.24.3.477
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    Cited by:

    1. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.

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