Solving a stochastic inventory-location problem using Lagrangian relaxation approach

This paper addresses the design of a supply network consisting of a supplier, a set of retailers and distribution centers to locate. In this supply network, each retailer faces a random demand of a single product and the supply lead-time from the supplier to distribution centers is random. The problem consists in selecting distribution centers to open in order to minimize inventory and safety stock costs at distribution centers, ordering costs and transportation costs across the network, and fixed facility location costs. The introduction of inventory costs and safety stock costs leads to difficult NP-hard non-linear combinatorial problem. A Lagrangian relaxation approach is proposed to generate efficient solutions and determine tight lower bounds. Numerical results show the efficiency of the proposed method.