Optimal inventory and admission policies for drop-shipping retailers serving in-store and online customers

This article studies the optimal inventory and dynamic admission policies of two physical retailers who, besides selling through their traditional in-store channels, also act as drop-shippers for an online retailer (e-tailer). The e-tailer carries no inventory of its own and always turns to one of the two physical retailers for order fulfillment. The considered scenario is the one in which retailer 1 (R1) and retailer 2 (R2) act as the primary and secondary drop-shippers of the e-tailer, respectively. While trying to maximize their respective revenues, both retailers face the problem of whether or not to accept the e-tailer's order-fulfillment request. It is initially assumed that the initial inventory levels of each retailer are fixed and that R1 shares his inventory information with R2. By adopting a revenue management framework, the dynamic admission policies of both retailers are studied and it is shown that R1 and R2 should implement one-dimensional and two-dimensional threshold policies, respectively. The scenario in which R1 does not share his inventory information with R2 is considered. For this scenario two heuristic policies for R2 are proposed and they are compared to the optimal policy when information is shared. A detailed sensitivity analysis for varying parameter value is presented, which shows the impact of information sharing between the two retailers. Finally, the assumption of fixed initial inventory levels is relaxed and the optimal initial inventory levels of each retailer that maximize their expected profits are determined.