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Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy

Author

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  • Bernd Heidergott

    (Department of Econometrics and Operations Research and Tinbergen Institute, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands)

  • Taoying Farenhorst-Yuan

    (Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands)

Abstract

We consider multicomponent maintenance systems with an F -failure group age-replacement policy: it keeps failed components idling until F components are failed and then replaces all failed components together with the nonfailed components whose age has passed the critical threshold age (theta) n for components of type n . With each maintenance action, costs are associated. We derive various unbiased gradient estimators based on the measure-valued differentiation approach for the gradient of the average cost. Each estimator has its own domain of applicability. We also compare the performance of our gradient estimators when applied to stochastic optimization with other general gradient-free methods.

Suggested Citation

  • Bernd Heidergott & Taoying Farenhorst-Yuan, 2010. "Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy," Operations Research, INFORMS, vol. 58(3), pages 706-718, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:706-718
    DOI: 10.1287/opre.1090.0760
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    References listed on IDEAS

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    1. Bernd Heidergott & Arie Hordijk & Heinz Weisshaupt, 2006. "Measure-Valued Differentiation for Stationary Markov Chains," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 154-172, February.
    2. Rommert Dekker & J. Robert van der Meer & Raymond Ph. Plasmeijer & Ralph E. Wildeman & Jacco J. de Bruin, 1996. "Maintenance of Light Standards, a Case-Study," Tinbergen Institute Discussion Papers 96-166/9, Tinbergen Institute.
    3. Robin P. Nicolai & Rommert Dekker, 2008. "Optimal Maintenance of Multi-component Systems: A Review," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 11, pages 263-286, Springer.
    4. Philip Heidelberger & Xi-Ren Cao & Michael A. Zazanis & Rajan Suri, 1988. "Convergence Properties of Infinitesimal Perturbation Analysis Estimates," Management Science, INFORMS, vol. 34(11), pages 1281-1302, November.
    5. Peter W. Glynn & Ward Whitt, 1992. "The Asymptotic Efficiency of Simulation Estimators," Operations Research, INFORMS, vol. 40(3), pages 505-520, June.
    6. B. Heidergott & F. J. Vázquez-Abad, 2008. "Measure-Valued Differentiation for Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 187-209, February.
    7. Paul Glasserman, 1991. "Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices," Operations Research, INFORMS, vol. 39(5), pages 724-738, October.
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    Cited by:

    1. Lin, Danping & Jin, Baoping & Chang, Daofang, 2020. "A PSO approach for the integrated maintenance model," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    3. Abderrahmane Abbou & Viliam Makis, 2019. "Group Maintenance: A Restless Bandits Approach," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 719-731, October.

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