A two-location lateral transshipment problem with customer switching

Lateral transshipments in multi-echelon stochastic inventory systems imply that locations at the same echelon of a supply chain share inventories in some way, in order to deal with local uncertainties in demands. While the structure of a transshipment policy will depend on many important factors, a commonly observed phenomenon at the retail level, called “customer switching”, may be of some significance. Under such a phenomenon, a customer, who cannot obtain a desired product at a specific location, may visit one or more other retail locations in search of the item. We consider the inventory replenishment and transshipment decisions in the presence of such stochastic “customer switching” behavior, for two firms which are either under centralized control, or operate independently.The first model adopted in this study considers two retailers that sell the same product to retail customers. After demand is realized, transshipments occur if only one location has insufficient inventory. Under this circumstance, a random fraction of the unfulfilled demand from the stocked out firm (which we refer to as the “shortage firm”) may switch to the other firm with surplus inventory (which we refer to as the “surplus firm”). We examine the impact of such customer switching behavior on the firms’ inventory decisions. We identify situations when the firm with surplus inventory is willing to (1) transship the entire quantity requested (“complete pooling policy”), (2) transship a portion of the amount requested (“inventory keeping policy”), or (3) transship nothing (“no-shipping policy”) to the shortage firm. We demonstrate that a unique pair of optimal order quantities exist if the two firms are centeredly coordinated. When the firms operate independently, we derive a sufficient condition for the existence of a unique equilibrium replenishment order quantity pair.We also explore the optimal shortage or excess reporting policy when inventory information is asymmetric. Since the firm with a surplus makes a transshipment decision based on the magnitude of the shortage at the other location, it is possible that the shortage firm reports to the surplus firm some desired shortage quantity, instead of the real shortage. We prove that there is a possibility that the underreporting situation exists.