Incorporating Inventory and Routing Costs in Strategic Location Models

Zuo-Jun Max Shen
Lian Qi, Missouri University of Science and Technology

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We consider a supply chain design problem where the decision maker needs to decide the number and previous termlocationsnext term 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 previous termcostnext term that includes previous termlocation costs and inventory costsnext term at the DCs, and distribution previous termcostsnext term in the supply chain. We show that this problem can be formulated as a nonlinear integer programming previous termmodel,next term 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 previous termlocation, inventory, and routingnext term decisions in the same optimization previous termmodel.