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A Two-State Partially Observable Markov Decision Process with Uniformly Distributed Observations

Author

Listed:
  • Abraham Grosfeld-Nir

    (Tel Aviv University, Tel Aviv, Israel)

Abstract

A controller observes a production system periodically, over time. If the system is in the GOOD state during one period, there is a constant probability that it will deteriorate and be in the BAD state during the next period (and remains there). The true state of the system is unobservable and can only be inferred from observations (quality of output). Two actions are available: CONTINUE or REPLACE (for a fixed cost). The objective is to maximize the expected discounted value of the total future income. For both the finite- and infinite-horizon problems, the optimal policy is of a CONTROL LIMIT (CLT) type: continue if the good state probability exceeds the CLT, and replace otherwise. The computation of the CLT involves a functional equation. An analytical solution for this equation is as yet unknown.For uniformly distributed observations we obtain the infinite-horizon CLT analytically . We also show that the finite horizon CLTs, as a function of the time remaining, are not necessarily monotone, which is counterintuitive.

Suggested Citation

  • Abraham Grosfeld-Nir, 1996. "A Two-State Partially Observable Markov Decision Process with Uniformly Distributed Observations," Operations Research, INFORMS, vol. 44(3), pages 458-463, June.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:3:p:458-463
    DOI: 10.1287/opre.44.3.458
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    Citations

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    Cited by:

    1. Akcay, Alp, 2022. "An alert-assisted inspection policy for a production process with imperfect condition signals," European Journal of Operational Research, Elsevier, vol. 298(2), pages 510-525.
    2. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    3. Givon, Moshe & Grosfeld-Nir, Abraham, 2008. "Using partially observed Markov processes to select optimal termination time of TV shows," Omega, Elsevier, vol. 36(3), pages 477-485, June.
    4. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    5. Hao Zhang & Weihua Zhang, 2023. "Analytical Solution to a Partially Observable Machine Maintenance Problem with Obvious Failures," Management Science, INFORMS, vol. 69(7), pages 3993-4015, July.
    6. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
    7. Grosfeld-Nir, Abraham, 2007. "Control limits for two-state partially observable Markov decision processes," European Journal of Operational Research, Elsevier, vol. 182(1), pages 300-304, October.

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