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.