Incorporating inventory and routing costs in strategic location models

Zuo Jun Shen, Lian Qi

Research output: Contribution to journalArticlepeer-review

221 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)372-389
Number of pages18
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Jun 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


  • Integrated supply chain design models
  • Inventory
  • Location models
  • Vehicle routing


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