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

T. W. Archibald (), D. P. Black () and K. D. Glazebrook ()
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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

Operations Research, 2009, vol. 57, issue 2, 314-326

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.

Keywords: dynamic programming/optimal control; applications; models; inventory/production; policies; probability; stochastic model applications (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (8)

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