IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v212y2011i1p131-140.html
   My bibliography  Save this article

Finite horizon semi-Markov decision processes with application to maintenance systems

Author

Listed:
  • Huang, Yonghui
  • Guo, Xianping

Abstract

This paper investigates finite horizon semi-Markov decision processes with denumerable states. The optimality is over the class of all randomized history-dependent policies which include states and also planning horizons, and the cost rate function is assumed to be bounded below. Under suitable conditions, we show that the value function is a minimum nonnegative solution to the optimality equation and there exists an optimal policy. Moreover, we develop an effective algorithm for computing optimal policies, derive some properties of optimal policies, and in addition, illustrate our main results with a maintenance system.

Suggested Citation

  • Huang, Yonghui & Guo, Xianping, 2011. "Finite horizon semi-Markov decision processes with application to maintenance systems," European Journal of Operational Research, Elsevier, vol. 212(1), pages 131-140, July.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:1:p:131-140
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(11)00081-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fernando Luque-Vásquez & J. Minjárez-Sosa, 2005. "Semi-Markov control processes with unknown holding times distribution under a discounted criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 455-468, July.
    2. Çekyay, B. & Özekici, S., 2010. "Mean time to failure and availability of semi-Markov missions with maximal repair," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1442-1454, December.
    3. Singh, Sumeetpal S. & Tadic, Vladislav B. & Doucet, Arnaud, 2007. "A policy gradient method for semi-Markov decision processes with application to call admission control," European Journal of Operational Research, Elsevier, vol. 178(3), pages 808-818, May.
    4. Anna Jaśkiewicz, 2001. "An approximation approach to ergodic semi-Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 1-19, October.
    5. Eugene A. Feinberg, 2004. "Continuous Time Discounted Jump Markov Decision Processes: A Discrete-Event Approach," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 492-524, August.
    6. John W. Mamer, 1986. "Successive Approximations for Finite Horizon, Semi-Markov Decision Processes with Application to Asset Liquidation," Operations Research, INFORMS, vol. 34(4), pages 638-644, August.
    7. Diego Klabjan & Daniel Adelman, 2007. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 528-550, August.
    8. Love, C. E. & Zhang, Z. G. & Zitron, M. A. & Guo, R., 2000. "A discrete semi-Markov decision model to determine the optimal repair/replacement policy under general repairs," European Journal of Operational Research, Elsevier, vol. 125(2), pages 398-409, September.
    9. Gunter, Sevket & Swanson, Lloyd, 1987. "Semi-Markov dynamic programming approach to competitive bidding with state space reduction considerations," European Journal of Operational Research, Elsevier, vol. 32(3), pages 435-447, December.
    10. D. J. White, 1995. "Finite Horizon Markov Decision Processes with Uncertain Terminal Payoffs," Operations Research, INFORMS, vol. 43(5), pages 862-869, October.
    11. Nielsen, Lars Relund & Kristensen, Anders Ringgaard, 2006. "Finding the K best policies in a finite-horizon Markov decision process," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1164-1179, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    2. Sharafali, Moosa & Tarakci, Hakan & Kulkarni, Shailesh & Razack Shahul Hameed, Raja Abdul, 2019. "Optimal delivery due date for a supplier with an unreliable machine under outsourced maintenance," International Journal of Production Economics, Elsevier, vol. 208(C), pages 53-68.
    3. Antoine Jacquier & Hao Liu, 2017. "Optimal liquidation in a Level-I limit order book for large tick stocks," Papers 1701.01327, arXiv.org, revised Nov 2017.
    4. Fang Chen & Xianping Guo & Zhong-Wei Liao, 2022. "Optimal Stopping Time on Semi-Markov Processes with Finite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 408-439, August.
    5. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    6. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.
    2. Zhang, Xueqing & Gao, Hui, 2012. "Road maintenance optimization through a discrete-time semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 110-119.
    3. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.
    4. Guo R. & Ascher H. & Love E., 2001. "Towards Practical and Synthetical Modelling of Repairable Systems," Stochastics and Quality Control, De Gruyter, vol. 16(1), pages 147-182, January.
    5. Banerjee, Pradeep K. & Turner, T. Rolf, 2012. "A flexible model for the pricing of perishable assets," Omega, Elsevier, vol. 40(5), pages 533-540.
    6. Dehayem Nodem, F.I. & Kenné, J.P. & Gharbi, A., 2011. "Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems," International Journal of Production Economics, Elsevier, vol. 134(1), pages 271-282, November.
    7. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    8. Dimitrakos, T.D. & Kyriakidis, E.G., 2008. "A semi-Markov decision algorithm for the maintenance of a production system with buffer capacity and continuous repair times," International Journal of Production Economics, Elsevier, vol. 111(2), pages 752-762, February.
    9. Zhao, Yunfei & Huang, Linan & Smidts, Carol & Zhu, Quanyan, 2020. "Finite-horizon semi-Markov game for time-sensitive attack response and probabilistic risk assessment in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    10. Jonathan Patrick & Martin L. Puterman & Maurice Queyranne, 2008. "Dynamic Multipriority Patient Scheduling for a Diagnostic Resource," Operations Research, INFORMS, vol. 56(6), pages 1507-1525, December.
    11. Lars Relund Nielsen & Erik Jørgensen & Søren Højsgaard, 2011. "Embedding a state space model into a Markov decision process," Annals of Operations Research, Springer, vol. 190(1), pages 289-309, October.
    12. White, D. J., 1996. "The maximization of a function over the efficient set via a penalty function approach," European Journal of Operational Research, Elsevier, vol. 94(1), pages 143-153, October.
    13. A H Shirmohammadi & C E Love & Z G Zhang, 2003. "An optimal maintenance policy for skipping imminent preventive maintenance for systems experiencing random failures," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 40-47, January.
    14. A Ponchet & M Fouladirad & A Grall, 2011. "Maintenance policy on a finite time span for a gradually deteriorating system with imperfect improvements," Journal of Risk and Reliability, , vol. 225(2), pages 105-116, June.
    15. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
    16. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    17. Jun Fei & Eugene Feinberg, 2013. "Variance minimization for constrained discounted continuous-time MDPs with exponentially distributed stopping times," Annals of Operations Research, Springer, vol. 208(1), pages 433-450, September.
    18. Turner, Rolf & Banerjee, Pradeep & Shahlori, Rayomand, 2014. "Optimal Asset Pricing," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i11).
    19. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    20. Sayyideh Mehri Mousavi & Hesam Shams & Shahrzad Ahmadi, 2017. "Simultaneous optimization of repair and control-limit policy in condition-based maintenance," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 245-254, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:212:y:2011:i:1:p:131-140. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.