A logistics network design model with vendor managed inventory

In this paper, we study a logistics network design problem with vendor managed inventory in which the company is in charge of managing inventory for its downstream warehouses and retailers, and can choose whether to satisfy each retailer's demand. The problem incorporates the location, transportation, pricing, and warehouse-retailer echelon inventory replenishment decisions. Traditionally, these decisions are made separately. We formulate the problem as a set-packing model and solve it using branch-and-price. The pricing problem that arises from each iteration of the column generation procedure is an interesting nonlinear IP problem. We show the pricing problem can be solved in O(n2logn) time for each warehouse, where n is the number of retailers. The computational results shed insights on the benefits that the integrated approach can achieve significant profit improvement. The computational results also highlight the efficiency of the solution algorithm.