Abstract: This paper considers a two-echelon inventory system with N-Identical Stores and One-Distribution Center. The demands have the Negative Binomial Distribution and partial lost sales (PLS). Most pervious two-echelonmodels have assumed either Poisson or Normal demands,which are poor model for items with high demand rates. We develop the model and show optimal policies for an inventory system. It can supply effective decision support.

Key words: Distribution center, partial lost sales, special orders, coordinated control