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On undiscounted semi-Markov decision processes with absorbing states

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  • Prasenjit Mondal

    (Chandernagore Government College)

Abstract

Limiting ratio average (undiscounted) reward finite (state and action spaces) semi-Markov decision processes (SMDPs) with absorbing states are considered where all but one states are absorbing. We propose a realistic inspection model that suitably fits into the class of undiscounted SMDPs with absorbing states. Existence of an optimal semi-stationary policy (i.e., a semi-Markov policy independent of decision epoch counts) is proved. A linear programming algorithm is provided to compute such an optimal policy.

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  • Prasenjit Mondal, 2016. "On undiscounted semi-Markov decision processes with absorbing states," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 161-177, April.
    • Handle: RePEc:spr:mathme:v:83:y:2016:i:2:d:10.1007_s00186-015-0524-y
    DOI: 10.1007/s00186-015-0524-y
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    References listed on IDEAS

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    1. Cyrus Derman, 1962. "On Sequential Decisions and Markov Chains," Management Science, INFORMS, vol. 9(1), pages 16-24, October.
    2. Manfred Schäl, 1992. "On the Second Optimality Equation for Semi-Markov Decision Models," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 470-486, May.
    3. Prasenjit Mondal & Sagnik Sinha, 2015. "Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition Times," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-26.
    4. Chen, Dongyan & Trivedi, Kishor S., 2005. "Optimization for condition-based maintenance with semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 25-29.
    5. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    6. J. Flesch & F. Thuijsman & O. J. Vrieze, 1996. "Recursive Repeated Games with Absorbing States," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1016-1022, November.
    7. P. J. Schweitzer & A. Federgruen, 1978. "The Functional Equations of Undiscounted Markov Renewal Programming," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 308-321, November.
    8. Tapas K. Das & Abhijit Gosavi & Sridhar Mahadevan & Nicholas Marchalleck, 1999. "Solving Semi-Markov Decision Problems Using Average Reward Reinforcement Learning," Management Science, INFORMS, vol. 45(4), pages 560-574, April.
    9. 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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    Cited by:

    1. 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.
    2. Prasenjit Mondal, 2018. "Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs," Operational Research, Springer, vol. 18(2), pages 451-468, July.

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