TY - JOUR

T1 - Indexability and index heuristics for a simple class of inventory routing problems

AU - Archibald, T W

AU - Black, D

AU - Glazebrook, K D

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

U2 - 10.1287/opre.1070.0505

DO - 10.1287/opre.1070.0505

M3 - Journal article

VL - 57

SP - 314

EP - 326

JO - Operations Research

JF - Operations Research

SN - 0030-364X

ER -