Dynamic Pricing and Timing of Upgrades

Abstract

Upgrading is a travel industry practice used to mitigate supply-demand mismatches among products of different quality levels. Such upgrades are usually implemented either at the booking time or at the check-in time. In this paper, we consider dynamically-offered upgrades between the booking and the check-in times by a firm that sells two types of products (premium and regular). The firm decides on the timing and quantity of upgrades. Customers who purchased the regular product may be offered upgrades via notifications containing a link to an upgrade website. A regular product purchaser either accepts or rejects the upgrade offer after clicking the link and observing the upgrade fee (price) dynamically determined by the firm. The upgrades are time limited; when they are not profitable, the firm can stop them by deactivating the upgrade links. Formulating the firm’s revenue maximization problem as a dynamic program, we show that the optimal upgrade policy is of a pulsing type. The firm either maintains zero or the maximum number of upgrade links. We identify a condition under which both the optimal number of active links and the optimal upgrade fee are monotone with respect to the leftover capacities. We then propose and analyze four model variations to incorporate relevant business rules and customer behaviors. The first one has a restricted upgrade fee choice set. The second one has limited upgrade activation and deactivation (e.g., the firm activates and deactivates upgrade links only in the morning of a day, but adjusts upgrade fees dynamically throughout the day). The third one allows a stockout upward substitution, in which the firm can sell a premium product to an arriving regular customer at a discount if the regular product stocks out. The fourth one incorporates consumer choice behaviors. Through a systematic numerical study, we first quantify the revenue improvement from the industry-standard check-in upgrade to dynamic pricing and timing of upgrades. We then identify business contexts, in which the revenue improvement is significant. Finally, we examine the robustness of the optimal dynamic upgrade policy.