Optimal policies for transshipping inventory in a retail network

Motivated by recent reports of improved customer service facilitated by the use of transshipment to pool inventory, we develop a formal model that focuses on the role of transshipment in a system of n-retailers who stock a good. In addition, some stock may be kept at a warehouse. If a retailer faces a stockout, he makes an attempt to fill backorders by using a transshipment that may come either from the warehouse or from another retailer that has excess stock. We determine that the optimal transshipment policy is described by exactly one of five protocols, and that the choice among them can be made by evaluating a set of easily computable conditions. We also provide other structural results that help identify conditions under which a warehouse should be open: how this decision is influenced by the total number of retailers, and how this decision is related to the degree of correlation of demand between retailers.