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Inspection--Maintenance--Replacement Schedules Under Markovian Deterioration

Author

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  • Morton Klein

    (Columbia University)

Abstract

A problem of finding optimal policies for the management of systems whose deterioration can be expressed as a Markov chain is considered. Using methods due to Manne and Derman for sequential decision problems involving average cost per unit time criteria, it is shown that the problem can be formulated in linear programming terms.

Suggested Citation

  • Morton Klein, 1962. "Inspection--Maintenance--Replacement Schedules Under Markovian Deterioration," Management Science, INFORMS, vol. 9(1), pages 25-32, October.
    • Handle: RePEc:inm:ormnsc:v:9:y:1962:i:1:p:25-32
    DOI: 10.1287/mnsc.9.1.25
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    Citations

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    Cited by:

    1. Durango-Cohen, Pablo L., 2007. "A time series analysis framework for transportation infrastructure management," Transportation Research Part B: Methodological, Elsevier, vol. 41(5), pages 493-505, June.
    2. 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.
    3. Durango-Cohen, Pablo L. & Madanat, Samer M., 2008. "Optimization of inspection and maintenance decisions for infrastructure facilities under performance model uncertainty: A quasi-Bayes approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(8), pages 1074-1085, October.
    4. Wallace J. Hopp & Sung‐Chi Wu, 1988. "Multiaction maintenance under markovian deterioration and incomplete state information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 447-462, October.
    5. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    6. Madanat, S M & Durango, Pablo L & Guillaumot, Vincent M, 2002. "Adaptive Optimization of Infrastructure Maintenance and Inspection Decisions under Performance Model Uncertainty," University of California Transportation Center, Working Papers qt2jj604pk, University of California Transportation Center.
    7. Nooshin Salari & Viliam Makis, 2020. "Application of Markov renewal theory and semi‐Markov decision processes in maintenance modeling and optimization of multi‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 548-558, October.
    8. Ali Dogramaci & Nelson M. Fraiman, 2004. "Replacement Decisions with Maintenance Under Uncertainty: An Imbedded Optimal Control Model," Operations Research, INFORMS, vol. 52(5), pages 785-794, October.
    9. Bloch-Mercier, Sophie, 2002. "A preventive maintenance policy with sequential checking procedure for a Markov deteriorating system," European Journal of Operational Research, Elsevier, vol. 142(3), pages 548-576, November.
    10. Kurt, Murat & Kharoufeh, Jeffrey P., 2010. "Optimally maintaining a Markovian deteriorating system with limited imperfect repairs," European Journal of Operational Research, Elsevier, vol. 205(2), pages 368-380, September.
    11. Ouyang, Yanfeng & Madanat, Samer, 2006. "An analytical solution for the finite-horizon pavement resurfacing planning problem," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 767-778, November.

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