A Combined Inventory-Location Model for Distribution Network Design

Two important areas of decision-making in distribution system design involve facility loca-tion and inventory policy determination. Facility location analyzes questions such as howmany facilities should be opened, where they should be located, and which customers shouldbe assigned to which DCs. Inventory policy determination involves more tactical decisionssuch as the order quantities and frequencies at each level or echelon in the network. It isbelieved 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 thestrengths that each DC has to offer (e.g., lower labor rates, land costs, etc.). Likewise, whenthe locations of two facilities are known, a multi-echelon inventory policy can be designedbetter to incorporate the exact lead times and fixed costs between the facilities at eachlevel of the system. Despite this, the two problems are typically solved independently. Thisresearch addresses these problems together and investigates different heuristic methods forsolving a combined inventory-location model. We begin by presenting the background andformulation for each problem. These formulations are then combined to show how the twoproblems can be mathematically formulated together. Rather than solve the problem ex-actly, two heuristic methods using different philosophies are tested. We apply these heuristicmethods to the combined inventory-location problem to determine how much we can im-prove distribution network design solutions and what type of heuristic methodology is mosteffective 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 witha fixed inventory policy. The improvement based on the data sets tested in this researchwas approximately $60,000. However, in cases where the inventory costs are a larger portionof 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 statisticallysignificant improved results over our first heuristic method. Moreover, the second heuristicmethod 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 insupply chain costs. As much as $174,000 was saved in the data sets tested for this research.