One-warehouse multiretailer systems with centralized stock information

We consider a distribution system with a central warehouse and multiple retailers. The warehouse orders from an outside supplier and replenishes the retailers which in turn satisfy customer demand. The retailers are nonidentical, and their demand processes are independent compound Poisson. There are economies of scale in inventory replenishment, which is controlled by an echelon-stock, batch-transfer policy. For the special case with simple Poisson demand, we develop an exact method for computing the long-run average holding and backorder costs of the system. Based on this exact method, we provide approximations for compound Poisson demand. Numerical examples are used to illustrate the accuracy of the approximations. We also present a numerical comparison between the average costs of a heuristic, echelon-stock policy and an existing lower bound on the average costs of all feasible policies.