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Turnpike Planning Horizons for a Markovian Decision Model

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  • Jeremy F. Shapiro

    (Massachusetts Institute of Technology)

Abstract

This paper establishes some asymptotic properties of the finite state and action space Markovian decision model. For the discounted case, a turnpike theorem is proven which states that an optimal immediate decision when the planning horizon is sufficiently large is to choose one of the decisions which is optimal when the planning horizon is infinite. An upper bound on how large is sufficiently large is given. An asymptotic property of the model for discount factors in a neighborhood of one is also developed.

Suggested Citation

  • Jeremy F. Shapiro, 1968. "Turnpike Planning Horizons for a Markovian Decision Model," Management Science, INFORMS, vol. 14(5), pages 292-300, January.
  • Handle: RePEc:inm:ormnsc:v:14:y:1968:i:5:p:292-300
    DOI: 10.1287/mnsc.14.5.292
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    Cited by:

    1. Nuthall, Peter L., 1980. "A Survey of Methods for Determining A Planning Horizon," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 48(01), pages 1-15, April.
    2. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    3. Mark E. Lewis & Anand Paul, 2019. "Uniform Turnpike Theorems for Finite Markov Decision Processes," Management Science, INFORMS, vol. 44(4), pages 1145-1160, November.
    4. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    5. M. Jacobson & N. Shimkin & A. Shwartz, 2003. "Markov Decision Processes with Slow Scale Periodic Decisions," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 777-800, November.

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