Centralized ordering and allocation policies in a two-echelon system with non-identical warehouses

We consider a depot-warehouse distribution system in which demand occurs at the warehouse level. At the beginning of every period the depot places an order from an external supplier which arrives after a fixed lead time. The received order is then shipped to the warehouses. The depot itself does not hold any inventory. There are non-zero shipment lead times from the depot to the warehouses. Linear holding costs are incurred at the warehouses and unsatisfied demands are backlogged at a linear penalty cost. Our work is a generalization of earlier work by Eppen and Schrage, to allow for non-identical warehouses. We present a simple and easy-to-implement allocation policy and derive an explicit expression for the optimal order quantity under the inventory balance allocation assumption used earlier by other researchers. A computional study is presented to evaluate the accuracy of the proposed solution.