Optimal Control of Selling Channels for an Online Retailer with Cost-Per-Click Payments and Seasonal Products

The problem studied in this paper is a predigestion of the decision faced by online retailers (etailers) that advertise on publisher or comparison-shopping websites. An etailer may sell its product not only through its online and bricks-and-mortar stores, but also through the websites of one or more third parties. However, the etailer has to pay a certain amount to such third parties in an action-based payment scheme, such as a cost-per-click (CPC) scheme. Under the CPC scheme, payment is based solely on click-throughs, which means that the etailer pays only when a shopper clicks through to the product page of its website. Only a fraction of such clicks lead to actual sales. The extra cost that is associated with shoppers who first click through to the third-party websites makes them less attractive as customers than those who directly visit the etailer's online store. Moreover, the CPC rate for a prominent placement is normally set by competitive bidding, and thus varies over time. Therefore, the etailer needs to decide dynamically whether or not to list on a third-party website. The structural properties of the optimal policy are discussed, and numerical examples are given to show the revenue impact of dynamic listing control