Dynamic Pricing and Timing of Upgrades

Problem definition: We propose and study a dynamic upgrading framework as a way to mitigate supply-demand mismatches among products of different qualities. Dynamic upgrades from a regular product to a premium one are offered between booking and check-in times by a travel firm. A regular product purchaser receives an upgrade offer as a link to a website and may accept it after observing an upgrade fee dynamically determined by the firm on the website. These offers are time-limited; the firm can stop them by deactivating the links. We characterize the optimal timing, quantity and pricing of dynamic upgrades between the booking and check-in times. As a common practice, static upgrading has been implemented either at the booking or the check-in time. Travel firms have recently started to adopt dynamic upgrades, which attest to their importance in practice. Methodology/results: We formulate and solve the problem using dynamic programming with two profit maximization approaches: a capacitated (limited) or a costly upgrade model. We prove that two models are profit-equivalent and the optimal upgrade policies in both are of a pulsing type; either maintaining zero or the maximum number of upgrade links. Focusing on the easy-to-implement capacitated upgrade model, we propose four variations to incorporate relevant business rules: upgrade postponement, restricted upgrade fees, limited upgrade (de-)activation times, and stockout-induced upward substitution. Using multimodularity concepts, we compare optimal policies across model variations and establish monotonicity properties. Managerial implications: The equivalence of two dynamic upgrade formulations allows managers to adopt either one. The optimal policy structures and monotonicity properties help managers understand tradeoffs in dynamic upgrades. Through a comprehensive and systematic numerical study, we identify business contexts suitable for dynamic upgrades and quantify their profit improvements. Compared to the optimal profit with check-in upgrades, the profit improvement with dynamic upgrades, flexible upgrade fees, unlimited (de-)activations and upward substitutions is 5.52% on average and can be as high as 59.34%. We also provide an upgrade process framework that can be used in practice and discuss its customization and implementation.