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When to Switch? Index Policies for Resource Scheduling in Emergency Response

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  • Dong Li
  • Li Ding
  • Stephen Connor

Abstract

This study considers the scheduling of limited resources to a large number of jobs (e.g., medical treatment) with uncertain lifetimes and service times, in the aftermath of a mass casualty incident. Jobs are subject to triage at time zero, and placed into a number of classes. Our goal is to maximize the expected number of job completions. We propose an effective yet simple index policy based on Whittle’s restless bandits approach. The problem concerned features a finite and uncertain time horizon that is dependent upon the service policy, which also determines the decision epochs. Moreover, the number of job classes still competing for service diminishes over time. To the best of our knowledge, this is the first application of Whittle’s index policies to such problems. Two versions of Lagrangian relaxation are proposed in order to decompose the problem. The first is a direct extension of the standard Whittle’s restless bandits approach, while in the second the total number of job classes still competing for service is taken into account; the latter is shown to generalize the former. We prove the indexability of all job classes in the Markovian case, and develop closed‐form indices. Extensive numerical experiments show that the second proposal outperforms the first one (that fails to capture the dynamics in the number of surviving job classes, or bandits) and produces more robust and consistent results as compared to alternative heuristics suggested from the literature, even in non‐Markovian settings.

Suggested Citation

  • Dong Li & Li Ding & Stephen Connor, 2020. "When to Switch? Index Policies for Resource Scheduling in Emergency Response," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 241-262, February.
  • Handle: RePEc:bla:popmgt:v:29:y:2020:i:2:p:241-262
    DOI: 10.1111/poms.13105
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    References listed on IDEAS

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    Cited by:

    1. Rob Shone & Vincent A. Knight & Paul R. Harper, 2020. "A conservative index heuristic for routing problems with multiple heterogeneous service facilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 511-543, December.
    2. 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.
    3. José Niño-Mora, 2020. "A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    4. 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.
    5. Roberto Aringhieri & Patrick Hirsch & Marion S. Rauner & Melanie Reuter-Oppermanns & Margit Sommersguter-Reichmann, 2022. "Central European journal of operations research (CJOR) “operations research applied to health services (ORAHS) in Europe: general trends and ORAHS 2020 conference in Vienna, Austria”," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(1), pages 1-18, March.
    6. Jie Yang & Fang He & Xi Lin & Max Zuo‐Jun Shen, 2021. "Mechanism Design for Stochastic Dynamic Parking Resource Allocation," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3615-3634, October.

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