Incorporating inventory and routing costs in strategic location models

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.03.032 Byline: Zuo-Jun Max Shen (a), Lian Qi (b) Keywords: Location models; Vehicle routing; Inventory; Integrated supply chain design models Abstract: We consider a supply chain design problem where the decision maker needs to decide the number and locations of the distribution centers (DCs). Customers face random demand, and each DC maintains a certain amount of safety stock in order to achieve a certain service level for the customers it serves. The objective is to minimize the total cost that includes location costs and inventory costs at the DCs, and distribution costs in the supply chain. We show that this problem can be formulated as a nonlinear integer programming model, for which we propose a Lagrangian relaxation based solution algorithm. By exploring the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer programming problem that must be solved in solving the Lagrangian relaxation sub-problems. We present computational results for several instances of the problem with sizes ranging from 40 to 320 customers. Our results show the benefits of having an integrated supply chain design framework that includes location, inventory, and routing decisions in the same optimization model. Author Affiliation: (a) Department of Industrial Engineering and Operations Research, University of California, 4141 Etcheverry Hall, Berkeley, CA 94720-1777, USA (b) Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA Article History: Received 9 March 2005; Accepted 25 March 2006