A Capacitated Location-Inventory Model with Demand Selection

In this paper, we consider an integrated supply chain network design problem, which incorporates inventory and pricing decisions into the capacitated facility location model. We assume that each warehouse has a capacity limitation that limits the average demand flowing through the warehouse and that the supplier can choose whether to satisfy each potential retailer's demand. We formulate the problem as a nonlinear integer programming model and solve the model via a Lagrangian relaxation based approach. We develop an efficient algorithm to solve the subproblem that arises from the Lagrangian relaxation procedure. Finally, we conduct extensive computational experiments to test the performance of the algorithms proposed in this paper and provide the managerial insights based on the computational results.