IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v287y2020i2d10.1007_s10479-017-2686-x.html
   My bibliography  Save this article

Computing semi-stationary optimal policies for multichain semi-Markov decision processes

Author

Listed:
  • Prasenjit Mondal

    (Government General Degree College)

Abstract

We consider semi-Markov decision processes with finite state and action spaces and a general multichain structure. A form of limiting ratio average (undiscounted) reward is the criterion for comparing different policies. The main result is that the value vector and a pure optimal semi-stationary policy (i.e., a policy which depends only on the initial state and the current state) for such an SMDP can be computed directly from an optimal solution of a finite set (whose cardinality equals the number of states) of linear programming (LP) problems. To be more precise, we prove that the single LP associated with a fixed initial state provides the value and an optimal pure stationary policy of the corresponding SMDP. The relation between the set of feasible solutions of each LP and the set of stationary policies is also analyzed. Examples are worked out to describe the algorithm.

Suggested Citation

  • Prasenjit Mondal, 2020. "Computing semi-stationary optimal policies for multichain semi-Markov decision processes," Annals of Operations Research, Springer, vol. 287(2), pages 843-865, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-017-2686-x
    DOI: 10.1007/s10479-017-2686-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-017-2686-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-017-2686-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Prasenjit Mondal, 2016. "On undiscounted semi-Markov decision processes with absorbing states," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 161-177, April.
    2. Manfred Schäl, 1992. "On the Second Optimality Equation for Semi-Markov Decision Models," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 470-486, May.
    3. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    4. William S. Jewell, 1963. "Markov-Renewal Programming. II: Infinite Return Models, Example," Operations Research, INFORMS, vol. 11(6), pages 949-971, December.
    5. William S. Jewell, 1963. "Markov-Renewal Programming. I: Formulation, Finite Return Models," Operations Research, INFORMS, vol. 11(6), pages 938-948, December.
    6. A. Jaśkiewicz, 2004. "On the Equivalence of Two Expected Average Cost Criteria for Semi-Markov Control Processes," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 326-338, May.
    7. Chen, Dongyan & Trivedi, Kishor S., 2005. "Optimization for condition-based maintenance with semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 25-29.
    8. Truman Bewley & Elon Kohlberg, 1978. "On Stochastic Games with Stationary Optimal Strategies," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 104-125, May.
    9. A. Hordijk & L. C. M. Kallenberg, 1979. "Linear Programming and Markov Decision Chains," Management Science, INFORMS, vol. 25(4), pages 352-362, April.
    10. Cyrus Derman, 1962. "On Sequential Decisions and Markov Chains," Management Science, INFORMS, vol. 9(1), pages 16-24, October.
    11. Prasenjit Mondal & Sagnik Sinha, 2015. "Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition Times," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-26.
    12. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, 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. Seyed Hossein Razavi Hajiagha & Jalil Heidary-Dahooie & Ieva Meidutė-Kavaliauskienė & Kannan Govindan, 2022. "A new dynamic multi-attribute decision making method based on Markov chain and linear assignment," Annals of Operations Research, Springer, vol. 315(1), pages 159-191, August.

    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. Prasenjit Mondal, 2016. "On undiscounted semi-Markov decision processes with absorbing states," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 161-177, April.
    2. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, December.
    3. Prasenjit Mondal, 2018. "Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs," Operational Research, Springer, vol. 18(2), pages 451-468, July.
    4. 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.
    5. 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.
    6. 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.
    7. B. Curtis Eaves & Arthur F. Veinott, 2014. "Maximum-Stopping-Value Policies in Finite Markov Population Decision Chains," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 597-606, August.
    8. Chris P. Lee & Glenn M. Chertow & Stefanos A. Zenios, 2008. "Optimal Initiation and Management of Dialysis Therapy," Operations Research, INFORMS, vol. 56(6), pages 1428-1449, December.
    9. Michael O’Sullivan & Arthur F. Veinott, Jr., 2017. "Polynomial-Time Computation of Strong and n -Present-Value Optimal Policies in Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 577-598, August.
    10. Dijk, N.M. van, 1989. "Truncation of Markov decision problems with a queueing network overflow control application," Serie Research Memoranda 0065, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    11. Huixia Huo, 2024. "Optimal Corrective Maintenance Policies via an Availability-Cost Hybrid Factor for Software Aging Systems," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    12. 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).
    13. Zhou, Zhi-Jie & Hu, Chang-Hua & Xu, Dong-Ling & Chen, Mao-Yin & Zhou, Dong-Hua, 2010. "A model for real-time failure prognosis based on hidden Markov model and belief rule base," European Journal of Operational Research, Elsevier, vol. 207(1), pages 269-283, November.
    14. Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    15. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    16. Jérôme Renault & Xavier Venel, 2017. "Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 349-376, May.
    17. Ahmadi, Reza & Newby, Martin, 2011. "Maintenance scheduling of a manufacturing system subject to deterioration," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1411-1420.
    18. Olde Keizer, Minou & Teunter, Ruud, 2014. "Opportunistic condition-based maintenance and aperiodic inspections for a two-unit series system," Research Report 14033-OPERA, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    19. 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.
    20. Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.

    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:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-017-2686-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.