Integrated warehouse location and inventory decisions in a three-tier distribution system

A three-tier distribution network which consists of a single supplier at a given location, a single intermediate warehouse whose location is to be determined, and multiple retailers at given locations is examined. The problem is the integration of warehouse location and inventory replenishment decisions with the objective of minimizing the system-wide transportation and inventory-related costs. The case where the inventory replenishment decisions are coordinated using a power-of-two policy is considered and a mathematical model for the simultaneous computation of the warehouse coordinates and coordinated replenishment policy parameters is developed. The analytical properties of the integrated location-inventory model are characterized and efficient solution methods that rely on these properties are developed. Computational results demonstrating the performance of the proposed heuristic methods and the potential practical impact of integrated decision making for location and inventory decisions are reported. These results indicate that the proposed methods are capable of effectively producing high-quality power-of-two solutions within 6% of the lower bound for the instances tested. The presented analysis is also useful for identifying: (i) the level of interaction between these two types of decisions that are treated separately in the traditional literature; and (ii) problem settings where the integrated location-inventory model offers significant cost savings.