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.