We consider an integrated distribution network design problem in which all the retailers face uncertain demand. The risk-pooling benefit is achieved by allowing some of the retailers to operate as distribution centers (DCs) with commitment in service level. The target is to minimize the expected total cost resulted from the DC location, transportation, and inventory. We formulate it as a two-stage nonlinear discrete stochastic optimization problem. The first stage decides which retailers to be selected as DCs and the second stage deals with the costs of DC-retailer assignment, transportation, and inventory.
In the literature, the similar models require the demands of all retailers in each scenario to have their variances identically proportional to their means. In this paper, we remove this restriction. We reformulate the problem as a set-covering model and solve it by a column generation approach. With a variable fixing technique, we are able to efficiently solve problems of moderate-size (up to one hundred retailers and nine scenarios).