An integrated supply chain problem: a nested lagrangian relaxation approach

The integration of tactical‐level with strategic‐level decisions in the supply chain represents an opportunity for substantial cost savings and provides a means for companies to gain a competitive advantage. Much of the previous research on supply chain network design has handled facility location decisions and inventory management decisions independently. In this paper, we develop a new joint facility location inventory model that is based on an approximate one‐warehouse multi‐retailer inventory model for each warehouse, and on the uncapacitated facility location problem. The proposed integer programming model simultaneously makes decisions pertaining to location and inventory policies on two echelons of the supply chain, the warehouse and the retailers. We develop two Lagrangian‐relaxation‐based algorithms to solve this model, and compare their performance to that of a conventional branch‐and‐bound algorithm on randomly generated problems.