Optimal Position-Based Warehouse Ordering in Divergent Two-Echelon Inventory Systems

A continuous–review two–echelon inventory system with one central warehouse and a number of nonidentical retailers is considered. The retailers face independent Poisson demand and apply standard (R, Q) policies. The retailer order quantities are fixed integer multiples of a certain batch size, representing the smallest pallet or container size transported in the system. A warehouse order may consist of one or several such batches. We derive a new policy for warehouse ordering, which is optimal in the broad class of position–based policies relying on complete information about the retailer inventory positions, transportation times, cost structures, and demand distributions at all facilities. The exact analysis of the new policy includes a method for determining the expected total inventory holding and backorder costs for the entire system. The class of position–based policies encompasses both the traditional installation–stock and echelon–stock (R, Q) policies, as well as the more sophisticated policies recently analyzed in the literature. The value of more carefully incorporating a richer information structure into the warehouse ordering policy is illustrated in a numerical study.