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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
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    Cited by:

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    2. 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.
    3. José Niño-Mora, 2022. "Multi-Gear Bandits, Partial Conservation Laws, and Indexability," Mathematics, MDPI, vol. 10(14), pages 1-31, July.
    4. 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.
    5. José Niño-Mora, 2020. "A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    6. 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.
    7. 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).
    8. 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.
    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.

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