Abstract: When a traditional supplier extends her business from the single channel of in-store retailers to the multi-channel of in-store retailers and e-retailers,she needs to expand her logistics system to supply the new demands from online customers. This paper considers a two-echelon logistics system consisting of a center warehouse and several district warehouses A capacity expansion and allocation model (CEAM) is developed with the structure of current logistics system unchanged.And a Lagrangian relaxation algorithm is designed to solve CEAM. Numerical experiments show the efficiency of the algorithm and illustrate the trade off between transportation cost and inventory pooling effect when searching for the optimal solution.

Key words: multi-channel supply chain, network location, inventory management, E-business