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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 baseddoi:10.1155/2019/2143042 fatcat:f36xwwfqq5dlblqi2oxtrcxdha