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Linear Programming in a Markov Chain

Author

Listed:
  • Philip Wolfe

    (The Rand Corporation, Santa Monica, California)

  • G. B. Dantzig

    (The Rand Corporation, Santa Monica, California)

Abstract

An infinite Markov process with a finite number of states is studied in which the transition probabilities for each state range independently over sets that are either finite or are convex polyhedra. A finite computational procedure is given for choosing those transition probabilities that minimize appropriate functions of the resulting equilibrium probabilities, the procedure is a specialization of the authors' decomposition algorithm for linear programming problems of special structure.

Suggested Citation

  • Philip Wolfe & G. B. Dantzig, 1962. "Linear Programming in a Markov Chain," Operations Research, INFORMS, vol. 10(5), pages 702-710, October.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:5:p:702-710
    DOI: 10.1287/opre.10.5.702
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    Cited by:

    1. K. Helmes & R. H. Stockbridge, 2000. "Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 107-127, July.
    2. Lauren B. Davis & Thom J. Hodgson & Russell E. King & Wenbin Wei, 2009. "Technical note: A computationally efficient algorithm for undiscounted Markov decision processes with restricted observations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 86-92, February.
    3. Vladimir Rykov & Olga Kochueva & Yaroslav Rykov, 2021. "Preventive Maintenance of the k -out-of- n System with Respect to Cost-Type Criterion," Mathematics, MDPI, vol. 9(21), pages 1-15, November.

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