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Linear Programming and Markov Decision Chains

Author

Listed:
  • A. Hordijk

    (University of Leiden, The Netherlands)

  • L. C. M. Kallenberg

    (University of Leiden, The Netherlands)

Abstract

In this paper we show that for a finite Markov decision process an average optimal policy can be found by solving only one linear programming problem. Also the relation between the set of feasible solutions of the linear program and the set of stationary policies is analyzed.

Suggested Citation

  • A. Hordijk & L. C. M. Kallenberg, 1979. "Linear Programming and Markov Decision Chains," Management Science, INFORMS, vol. 25(4), pages 352-362, April.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:352-362
    DOI: 10.1287/mnsc.25.4.352
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    Citations

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    Cited by:

    1. Guillot, Matthieu & Stauffer, Gautier, 2020. "The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective," European Journal of Operational Research, Elsevier, vol. 285(1), pages 148-158.
    2. Prasenjit Mondal, 2020. "Computing semi-stationary optimal policies for multichain semi-Markov decision processes," Annals of Operations Research, Springer, vol. 287(2), pages 843-865, April.
    3. Jérôme Renault & Xavier Venel, 2017. "Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 349-376, May.
    4. Purba Das & T. Parthasarathy & G. Ravindran, 2022. "On Completely Mixed Stochastic Games," SN Operations Research Forum, Springer, vol. 3(4), pages 1-26, December.
    5. Lodewijk Kallenberg, 2013. "Derman’s book as inspiration: some results on LP for MDPs," Annals of Operations Research, Springer, vol. 208(1), pages 63-94, September.
    6. Tetsuichiro Iki & Masayuki Horiguchi & Masami Kurano, 2007. "A structured pattern matrix algorithm for multichain Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 545-555, December.
    7. Dmitry Krass & O. J. Vrieze, 2002. "Achieving Target State-Action Frequencies in Multichain Average-Reward Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 545-566, August.
    8. Daniel F. Silva & Bo Zhang & Hayriye Ayhan, 2018. "Admission control strategies for tandem Markovian loss systems," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 35-63, October.
    9. Vivek S. Borkar & Vladimir Gaitsgory, 2019. "Linear Programming Formulation of Long-Run Average Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 101-125, April.
    10. B. Curtis Eaves & Arthur F. Veinott, 2014. "Maximum-Stopping-Value Policies in Finite Markov Population Decision Chains," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 597-606, August.
    11. Michael O’Sullivan & Arthur F. Veinott, Jr., 2017. "Polynomial-Time Computation of Strong and n -Present-Value Optimal Policies in Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 577-598, August.
    12. Yang, Hai & Zhou, Jing, 1998. "Optimal traffic counting locations for origin-destination matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 109-126, February.
    13. Dijk, N.M. van, 1989. "Truncation of Markov decision problems with a queueing network overflow control application," Serie Research Memoranda 0065, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    14. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    15. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, December.

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