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Optimal Stopping in a Partially Observable Markov Process with Costly Information

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  • George E. Monahan

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

A problem of optimal stopping in a Markov chain whose states are not directly observable is presented. Using the theory of partially observable Markov decision processes, a model which combines the classical stopping problem with sequential sampling at each stage of the decision process is developed. Several results which characterize the optimal expected value function in terms of its parameters are given. An example is given which indicates that the best action to take as a function of the information currently available may not be of the intuitively appealing control limit type. The set of states at which it is optimal to purchase information need not be convex. The expected value of information as a function of the decision maker's knowledge is related to nonmonotone optimal policies.

Suggested Citation

  • George E. Monahan, 1980. "Optimal Stopping in a Partially Observable Markov Process with Costly Information," Operations Research, INFORMS, vol. 28(6), pages 1319-1334, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1319-1334
    DOI: 10.1287/opre.28.6.1319
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    Cited by:

    1. van Staden, Heletjé E. & Boute, Robert N., 2021. "The effect of multi-sensor data on condition-based maintenance policies," European Journal of Operational Research, Elsevier, vol. 290(2), pages 585-600.
    2. Yee, Hannah & van Staden, Heletjé E. & Boute, Robert N., 2024. "Dual sourcing under non-stationary demand and partial observability," European Journal of Operational Research, Elsevier, vol. 314(1), pages 94-110.
    3. Fine, Charles H. & Li, Lode., 1986. "A stochastic theory of exit and stopping time equilibria," Working papers 1755-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Fan, Xiaoli & Gómez, Miguel & Atallah, Shadi, 2016. "Optimal Monitoring and Controlling of Invasive Species: The Case of Spotted Wing Drosophila in the United States," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 236042, Agricultural and Applied Economics Association.
    5. Churlzu Lim & J. Neil Bearden & J. Cole Smith, 2006. "Sequential Search with Multiattribute Options," Decision Analysis, INFORMS, vol. 3(1), pages 3-15, March.
    6. Chhabra, Meenal & Das, Sanmay & Sarne, David, 2014. "Expert-mediated sequential search," European Journal of Operational Research, Elsevier, vol. 234(3), pages 861-873.
    7. Weber, Thomas A. & Nguyen, Viet Anh, 2018. "A linear-quadratic Gaussian approach to dynamic information acquisition," European Journal of Operational Research, Elsevier, vol. 270(1), pages 260-281.
    8. Debarun Bhattacharjya & Léa A. Deleris, 2014. "The Value of Information in Some Variations of the Stopping Problem," Decision Analysis, INFORMS, vol. 11(3), pages 189-203, September.

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