IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v31y2019i4p719-731.html
   My bibliography  Save this article

Group Maintenance: A Restless Bandits Approach

Author

Listed:
  • Abderrahmane Abbou

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • Viliam Makis

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

Abstract

We consider a maintenance planner problem to dynamically allocate the available repairmen to a system of unreliable production facilities. Each facility has several machines that incur a linear production loss due to stochastic degradation, which we model as a continuous time Markov process with fully observable states. The objective is to schedule group maintenance interventions, in discrete time epochs, so as to minimize production losses over an infinite horizon. Direct solution procedures, such as dynamic programming value or policy iteration, are impractical due to the curse of dimensionality. An approximate scheduling procedure is developed following Whittle’s restless bandits approach. In particular, we decompose the Whittle’s relaxation of our scheduling problem by production facility (i.e., bandit) using the Lagrangian technique. Based on the structural investigation of a single-bandit problem, we prove indexability and propose a novel index computational algorithm. Our numerical study shows that, for systems with three or four facilities, the index policy has a near-zero optimality gap. For systems with 10 or more facilities, the index policy expected cost remains fairly close to a lower bound that we compute using the known linear programming (LP) formulation of Whittle’s relaxation. Furthermore, the numerical study also shows that our policy yields substantial expected cost improvements relative to a benchmark LP-based heuristic when the states are partially observable and can handle large-scale systems unlike LP-based heuristics, which have excessive memory requirements.

Suggested Citation

  • Abderrahmane Abbou & Viliam Makis, 2019. "Group Maintenance: A Restless Bandits Approach," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 719-731, October.
  • Handle: RePEc:inm:orijoc:v:31:y:2019:i:4:p:719-731
    DOI: 10.1287/ijoc.2018.0863
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0863
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2018.0863?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
    ---><---

    References listed on IDEAS

    as
    1. Christos H. Papadimitriou & John N. Tsitsiklis, 1999. "The Complexity of Optimal Queuing Network Control," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 293-305, May.
    2. Philip Cho & Vivek Farias & John Kessler & Retsef Levi & Thomas Magnanti & Eric Zarybnisky, 2015. "Maintenance and flight scheduling of low observable aircraft," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 60-80, February.
    3. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    4. Dimitris Bertsimas & José Niño-Mora, 2000. "Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic," Operations Research, INFORMS, vol. 48(1), pages 80-90, February.
    5. Darina Graczová & Peter Jacko, 2014. "Generalized Restless Bandits and the Knapsack Problem for Perishable Inventories," Operations Research, INFORMS, vol. 62(3), pages 696-711, June.
    6. 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.
    7. Peter Ritchken & John G. Wilson, 1990. "(m,T) Group Maintenance Policies," Management Science, INFORMS, vol. 36(5), pages 632-639, May.
    8. Liu, Gia-Shie, 2011. "Dynamic group instantaneous replacement policies for unreliable Markovian service systems," International Journal of Production Economics, Elsevier, vol. 130(2), pages 203-217, April.
    9. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    10. 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.
    11. Olde Keizer, Minou C.A. & Flapper, Simme Douwe P. & Teunter, Ruud H., 2017. "Condition-based maintenance policies for systems with multiple dependent components: A review," European Journal of Operational Research, Elsevier, vol. 261(2), pages 405-420.
    12. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.
    13. 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.
    14. Shafiee, Mahmood, 2015. "Maintenance logistics organization for offshore wind energy: Current progress and future perspectives," Renewable Energy, Elsevier, vol. 77(C), pages 182-193.
    15. Seyed M.R. Iravani & Izak Duenyas & Tava Lennon Olsen, 2000. "A Production/Inventory System Subject to Failure with Limited Repair Capacity," Operations Research, INFORMS, vol. 48(6), pages 951-964, December.
    16. Haijun Li & Susan H. Xu, 2004. "On the Coordinated Random Group Replacement Policy in Multivariate Repairable Systems," Operations Research, INFORMS, vol. 52(3), pages 464-477, June.
    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. José Niño-Mora, 2020. "A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    2. Azizi, Fariba & Salari, Nooshin, 2023. "A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    3. Urtzi Ayesta & Manu K. Gupta & Ina Maria Verloop, 2021. "On the computation of Whittle’s index for Markovian restless bandits," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 179-208, February.
    4. Liu, Bin & Pandey, Mahesh D. & Wang, Xiaolin & Zhao, Xiujie, 2021. "A finite-horizon condition-based maintenance policy for a two-unit system with dependent degradation processes," European Journal of Operational Research, Elsevier, vol. 295(2), pages 705-717.
    5. Zheng, Rui & Xing, Yuan & Ren, Xiangyun, 2023. "Multilevel preventive replacement for a system subject to internal deterioration, external shocks, and dynamic missions," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    6. José Niño-Mora, 2022. "Multi-Gear Bandits, Partial Conservation Laws, and Indexability," Mathematics, MDPI, vol. 10(14), pages 1-31, July.
    7. Ya‐Tang Chuang & Manaf Zargoush & Somayeh Ghazalbash & Saied Samiedaluie & Kerry Kuluski & Sara Guilcher, 2023. "From prediction to decision: Optimizing long‐term care placements among older delayed discharge patients," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1041-1058, April.
    8. José Niño-Mora, 2020. "Fast Two-Stage Computation of an Index Policy for Multi-Armed Bandits with Setup Delays," Mathematics, MDPI, vol. 9(1), pages 1-36, December.
    9. Xu, Jianyu & Liu, Bin & Zhao, Xiujie & Wang, Xiao-Lin, 2024. "Online reinforcement learning for condition-based group maintenance using factored Markov decision processes," European Journal of Operational Research, Elsevier, vol. 315(1), pages 176-190.

    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. Glazebrook, K. D. & Mitchell, H. M. & Ansell, P. S., 2005. "Index policies for the maintenance of a collection of machines by a set of repairmen," European Journal of Operational Research, Elsevier, vol. 165(1), pages 267-284, August.
    2. Turgay Ayer & Can Zhang & Anthony Bonifonte & Anne C. Spaulding & Jagpreet Chhatwal, 2019. "Prioritizing Hepatitis C Treatment in U.S. Prisons," Operations Research, INFORMS, vol. 67(3), pages 853-873, May.
    3. Petchrompo, Sanyapong & Parlikad, Ajith Kumar, 2019. "A review of asset management literature on multi-asset systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 181-201.
    4. Vishal Ahuja & John R. Birge, 2020. "An Approximation Approach for Response-Adaptive Clinical Trial Design," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 877-894, October.
    5. Liu, Gia-Shie, 2011. "Dynamic group instantaneous replacement policies for unreliable Markovian service systems," International Journal of Production Economics, Elsevier, vol. 130(2), pages 203-217, April.
    6. José Niño-Mora, 2023. "Markovian Restless Bandits and Index Policies: A Review," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    7. Gia-Shie Liu, 2019. "A Group Replacement Decision Support System Based on Internet of Things," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    8. Ece Zeliha Demirci & Joachim Arts & Geert-Jan Van Houtum, 2022. "A restless bandit approach for capacitated condition based maintenance scheduling," DEM Discussion Paper Series 22-01, Department of Economics at the University of Luxembourg.
    9. Erguido, A. & Crespo Márquez, A. & Castellano, E. & Gómez Fernández, J.F., 2017. "A dynamic opportunistic maintenance model to maximize energy-based availability while reducing the life cycle cost of wind farms," Renewable Energy, Elsevier, vol. 114(PB), pages 843-856.
    10. Giovanni Rinaldi & Philipp R. Thies & Lars Johanning, 2021. "Current Status and Future Trends in the Operation and Maintenance of Offshore Wind Turbines: A Review," Energies, MDPI, vol. 14(9), pages 1-28, April.
    11. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    12. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    13. Azizi, Fariba & Salari, Nooshin, 2023. "A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    14. Urtzi Ayesta & Manu K. Gupta & Ina Maria Verloop, 2021. "On the computation of Whittle’s index for Markovian restless bandits," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 179-208, February.
    15. 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.
    16. N. Knofius & M. C. Heijden & A. Sleptchenko & W. H. M. Zijm, 2021. "Improving effectiveness of spare parts supply by additive manufacturing as dual sourcing option," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 189-221, March.
    17. Liu, Gehui & Chen, Shaokuan & Ho, Tinkin & Ran, Xinchen & Mao, Baohua & Lan, Zhen, 2022. "Optimum opportunistic maintenance schedule over variable horizons considering multi-stage degradation and dynamic strategy," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    18. Dilaver, Halit Metehan & Akçay, Alp & van Houtum, Geert-Jan, 2023. "Integrated planning of asset-use and dry-docking for a fleet of maritime assets," International Journal of Production Economics, Elsevier, vol. 256(C).
    19. Chiel van Oosterom & Lisa M. Maillart & Jeffrey P. Kharoufeh, 2017. "Optimal maintenance policies for a safety‐critical system and its deteriorating sensor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 399-417, August.
    20. Song Lin & Juanjuan Zhang & John R. Hauser, 2015. "Learning from Experience, Simply," Marketing Science, INFORMS, vol. 34(1), pages 1-19, 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:inm:orijoc:v:31:y:2019:i:4:p:719-731. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.