Optimal Admission Polices for a Retailer of Seasonal Products with Drop-Shipping

This paper studies optimal inventory rationing policies for a retailer of perishable products who sells through its own stores and third party Websites by an affiliate program. By posting on partners\´ Webpages, an affiliate program allows the retailer to attract more customers who otherwise would be missed. However, the retailer needs to pay out a commission for each sale originated from the Website operator that participates in the affiliate program. Thus, the net revenue of selling one unit of product to an online "referral" (online customer) is less profitable than that to a customer from a physical store. When the inventory at stores is running low, the retailer may further refer the online request to somebody else for fulfilling, which is equivalently to say that the retailer can reject online customer requests. Therefore, upon the arrival of any demand through the affiliate program, the retailer needs to decide whether or not to accept it; and if so, assign which of multiple outlets for the fulfillment. Based on a discrete-time dynamic programming model, the optimal admission policy of the retailer is analyzed in this paper, which is shown to be a two-dimensional threshold policy. The structural properties of the revenue function are analyzed, and numerical examples are given to show the revenue impact of optimal admission control.