Logistics distribution network design with two commodity categories

In this paper, we study the design of a logistics distribution network consisting of a supplier, a set of potential warehouses, and a set of retailers. There are commodities from two product categories, that is, category A and category B, flowing across the network. The demand for commodities in product category A is stable. The demand for commodities in product category B is highly uncertain. We show that the network design problem to distribute the commodities in both product categories can be formulated as the uncapacitated facility location problem with monotone submodular costs and tackled using a cutting plane algorithm. We propose a strongly polynomial time algorithm for the nonlinear discrete optimization problem, which must be solved in each iteration of the cutting plane algorithm. We also provide the computational results, and summarize the insights based on the proposed model and the solution algorithm.