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Indexability and index heuristics for a simple class of inventory routing problems

Archibald, T W and Black, D and Glazebrook, K D (2009) Indexability and index heuristics for a simple class of inventory routing problems. Operations Research, 57. pp. 314-326. ISSN 0030-364X

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    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.

    Item Type: Article
    Journal or Publication Title: Operations Research
    Subjects:
    Departments: Lancaster University Management School > Management Science
    ID Code: 44980
    Deposited By: ep_importer_pure
    Deposited On: 11 Jul 2011 19:24
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Apr 2014 22:27
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/44980

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