A Combined Inventory-Location Model for Distribution Network Design

Two important areas of decision-making in distribution system design involve facility location and inventory policy determination. Facility location analyzes questions such as how many facilities should be opened, where they should be located, and which customers should be assigned to which DCs. Inventory policy determination involves more tactical decisions such as the order quantities and frequencies at each level or echelon in the network. It is believed that these two decisions can influence each other significantly. Including a multi-echelon inventory policy decision in a location analysis allows a user to capitalize on the strengths that each DC has to offer (e.g., lower labor rates, land costs, etc.). Likewise, when the locations of two facilities are known, a multi-echelon inventory policy can be designed better to incorporate the exact lead times and fixed costs between the facilities at each level of the system. Despite this, the two problems are typically solved independently. This research addresses these problems together and investigates different heuristic methods for solving a combined inventory-location model. We begin by presenting the background and formulation for each problem. These formulations are then combined to show how the two problems can be mathematically formulated together. Rather than solve the problem exactly, two heuristic methods using different philosophies are tested. We apply these heuristic methods to the combined inventory-location problem to determine how much we can improve distribution network design solutions and what type of heuristic methodology is most effective in gaining these improvements. Our results show that the combined inventory-location model is capable of improving on the solutions obtained by a location model with a fixed inventory policy. The improvement based on the data sets tested in this research was approximately $60,000. However, in cases where the inventory costs are a larger portion of the total cost, the improvement made by the inventory-location model increased to over $1,000,000. We also found that our second heuristic method tested provided statistically significant improved results over our first heuristic method. Moreover, the second heuristic method typically ran 67% faster. The improved results, although small in a relative sense (the average improvement was 0.18%), would still represent a large absolute improvement in supply chain costs. As much as $174,000 was saved in the data sets tested for this research.