An integrated model of the periodic delivery problems for vending-machine supply chains

In this paper we present a model and solution procedures of the Inventory Routing Problem (IRP) encountered in vending machine supply chains working under vendor-managed inventory (VMI) scheme. The new IRP model is built based on the existing Periodic Vehicle Routing Problem with Time-windows (PVRPTW). The model will be referred to as the Integrated Inventory and Periodic Vehicle Routing Problem with Time-windows (IPVRPTW). The objective of the IPVRPTW is to minimize the sum of the average inventory holding and traveling costs during a given m-day period. The visit frequency is treated as a decision variable instead of as a fixed parameter. We attempt to optimize the visit frequency of each retailer and to build vehicle tours simultaneously in order to find the best trade-off between the inventory holding and traveling costs. Computational experiments are conducted on some instances taken from the literature to evaluate the performance of the proposed model. 2004 Elsevier Ltd. All rights reserved.