Design of multi-commodity distribution network with random demands and supply lead-times

This paper deals with the stochastic multi-commodity distribution network design problem. The distribution network is composed of a single supplier serving a set of retailers through a set of distribution centers (DCs) to locate. Each retailer faces independent random demands of different commodities, the supply lead-time from the supplier to each DC is random. The central issues of the problem are: which retailer locations should be selected as DCs and commodity-by-commodity how to assign retailers to DCs. The goal is to minimize the total location, shipment, and inventory costs, while ensuring a specified retailer service level. A Lagrangian relaxation approach is proposed, and computational experiments presented and analyzed showing its effectiveness.