Analysis of a Two-Echelon Inventory Control System with Complete Redistribution

This paper examines a two-level distribution system consisting of a central warehouse (CW) supplying several branch warehouses (BW's), which, in turn, supply normally-distributed customer demands in a periodic-review environment. The CW replenishes system inventory using a base-stock replenishment policy and a predetermined order cycle of H time periods; i.e., every H periods, the CW orders enough from an outside supplier to bring the systemwide inventory position to a certain level (to be determined) based on a given minimum level of customer service. Upon receipt of this order, the CW allocates it entirely to the BW's so as to minimize the expected total units short at the BW's. This simple allocation scheme, may, of course, lead to out-of-balance BW inventories towards the end of the CW's order cycle. Hence, redistribution during the cycle should be considered. The redistribution treated here is a complete redistribution of all BW inventories one period before the end of the order cycle. Approximate formulas are derived which allow for a comparison of the system-wide inventories appropriate to each of two allocation schemes: (1) the simple allocation scheme only; and (2) the simple allocation scheme with total redistribution one period before the end of the order cycle. Limited computational tests indicate the magnitude of the improvements possible with total redistribution, and the sensitivities of these improvements to model parameters.