Croxton, Zinn take inventory of network design with new model
Taking stock of inventory costs could save corporations millions of dollars when it comes to mapping out their logistics networks.
For one national retailer, this could mean savings of up to 10 percent or $4.5 million annually by factoring inventory costs into the design of their distribution network, according to research by Keely Croxton, associate professor of logistics, and Walter Zinn, professor of logistics.
Companies frequently use optimization models to find the delicate balance between transportation costs and fixed warehouse costs, but these traditional models do not account for the cost of holding inventory in the network. However, having more stocking locations increases the inventory requirements, so inventory can impact what an optimal network would look like. By using traditional models that don’t include inventory costs, companies might be settling for a suboptimal distribution network. This research aimed to develop a model that included inventory costs and examine the impact that this would have on the optimal network.
Calculating inventory costs into network design generally reduced the number of warehouses when compared to a model based only on transportation and fixed warehouse costs, Croxton said. Inventory costs are reduced because the number of stocking locations is also reduced.
Companies with large distribution networks would benefit from the new model, because eliminating one or two warehouses could have a significant impact on trimming costs. Inventory costs had a bigger impact on companies with larger networks, rather than a system with just a few warehouses.
“An important implication of this result is that including inventory cost in network design is more beneficial, or even practical, when the number of warehouses currently in the network is relatively large,” Zinn said. “Considering inventory in these models has an impact on total cost when it results in a reduction in the number of warehouses. In a network with few warehouses, it is unlikely that considering inventory would make enough of a difference to reduce the number of warehouses.”
Croxton and Zinn’s article “Inventory Considerations in Network Design” will be honored next month with the Journal of Business Logistics’ Bernard J. La Londe Best Paper Award at the Supply Chain Management Educator’s Conference. The publication is recognized as the leading logistics and supply chain management professional journal.
“You have some flexibility with public warehousing and such, but basically companies design their networks looking at the longterm movement. With the environment changing and transportation costs changing it makes it an interesting proposition how you kind of keep on top of those costs.”

Keely Croxton

The study is the first to be published that simultaneously considers inventory costs, along with the traditional factors of transportation and fixed warehousing costs involved in establishing an optimal logistics network.
Using data obtained from a mediumsized national retailer based in the Midwest, Croxton and Zinn used 14 diverse and realistic scenarios in the study to compare the results of their model to the results of a traditional network design model. Each scenario considered the variability in demand as well as service levels for three product groups, inventory carrying costs, transportation costs, demand levels, warehouse costs and the product value.
To include inventory costs along with transportation and warehouse costs, the researchers developed a mathematical model which used the square root law to reflect the total inventory cost. They calculated inventory costs according to the square root law and added it to a standard network design model with limited impact on the size of the formulation.
Tapping into the square root law allowed Croxton and Zinn to take into account the impact that the number of warehouses has on systemwide inventory requirements. The actual warehouse locations of the retailer, which operates approximately 150 stores in 30 states, were used as input into the mathematical model.
“Using this on a real company’s data, we were able to solve it very quickly and because of the structure of the model and the square root law we know we can expand it to a much larger company,” Croxton said. “Because of the structure of the model, there’s no reason to believe you couldn’t take it to as big of a company as you wanted, as long as you make the same set of assumptions.”
With rising fuel costs forcing some trucking companies off the road and the United States’ sea ports packed with ships full of imported goods from Asia, Croxton said companies need to look at their network costs for the changing global marketplace.
“You have some flexibility with public warehousing and such, but basically companies design their networks with a longterm commitment in mind,” she said. “With the business environment and transportation costs changing it makes it an interesting proposition how you keep on top of those costs.”
Companies can take advantage of mathematical models to optimize their network in this dynamic environment, but they need to make sure that the models are capturing all their costs. Research like that conducted by Croxton and Zinn can help further develop such models and alert managers to the risks of using traditional models and not factoring in all cost elements.
