An Exact Performance Evaluation for the Supplier in a Two-Echelon Inventory System

This paper studies a continuous review two-echelon inventory system with a supplier serving multiple retailers. Each location uses a decentralized (Q, R) policy based on installation stocks. Each retailer may set a unique reorder quantity as a multiple of a basic packaging size Q. The supplier, in turn, adopts a similar batch replenishment policy. Our objective is to derive the exact steady-state performance for the supplier. We show that the inventory position at the supplier can be easily characterized by a uniform distribution. As a result, the closed-form expected cost function is tractable. We also examine the performance of approximation schemes such as the classic Poisson approximation. Our numerical results show that even though the Poisson approximation performs reasonably well in estimating steady-state performance, the cost penalty for using it in optimization may be significant.