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Indexability and Index Heuristics for a Simple Class of Inventory Routing Problems

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  • T. W. Archibald

    (Management School, University of Edinburgh, Edinburgh, EH8 9JY, United Kingdom)

  • D. P. Black

    (Management School, Lancaster University, Lancaster, LA1 4YX, United Kingdom)

  • K. D. Glazebrook

    (Management School, Lancaster University, Lancaster, LA1 4YX, United Kingdom)

Abstract

We utilise and develop Whittle's restless bandit formulation to analyse a simple class of inventory routing problems with direct deliveries. These routing problems arise from the practice of vendor-managed inventory replenishment and concern the optimal replenishment of a collection of inventory holding locations controlled centrally by a decision maker who is able to monitor inventory levels throughout the network. We develop a notion of location indexability from a Lagrangian relaxation of the problem and show that (subject to mild conditions) the locations are indeed indexable. We thus have a collection of location indices in closed form, namely, real-valued functions of the inventory level (one for each location), which measure in a natural way (namely, as a fair charge for replenishment) each location's priority for inclusion in each day's deliveries. We discuss how to use such location indices to construct heuristics for replenishment and assess a greedy index heuristic in a numerical study where it performs strongly. A simpler approximate index analysis is available for the case in which the demand at each location is Poisson. This analysis permits a more explicit characterisation of the range of holding cost rates for which (approximate) location indexability is guaranteed.

Suggested Citation

  • T. W. Archibald & D. P. Black & K. D. Glazebrook, 2009. "Indexability and Index Heuristics for a Simple Class of Inventory Routing Problems," Operations Research, INFORMS, vol. 57(2), pages 314-326, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:314-326
    DOI: 10.1287/opre.1070.0505
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    References listed on IDEAS

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    Cited by:

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    3. Li, Kunpeng & Chen, Bin & Sivakumar, Appa Iyer & Wu, Yong, 2014. "An inventory–routing problem with the objective of travel time minimization," European Journal of Operational Research, Elsevier, vol. 236(3), pages 936-945.
    4. Nicolas Gast & Bruno Gaujal & Kimang Khun, 2023. "Testing indexability and computing Whittle and Gittins index in subcubic time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 391-436, June.
    5. 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.
    6. Vivek S. Borkar & Sarath Pattathil, 2022. "Whittle indexability in egalitarian processor sharing systems," Annals of Operations Research, Springer, vol. 317(2), pages 417-437, October.
    7. 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.
    8. 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.

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