Much of the recent revenue management literature takes customer behavior into account. A number of parametric models that incorporate customer choice have been developed. In some cases, these models closely approximate reality and provide high quality solutions. Nevertheless, most studies of revenue management models do not consider the possibility that the model used to generate decisions is different from reality. Such analyses also typically do not address effects of forecasting or how forecasts evolve when the model being used is misspecified. (A model for which there is no parameter setting that makes the model a correct description of reality is called a misspecified model). In this dissertation, we study some models of customer choice in revenue management and test their performance when implemented in settings where their assumptions are violated; i.e., when they are misspecified.
First, we study a model based on the notion of "buy-up" that considers the dependency of the customers who are willing to purchase low-fare tickets and those who prefer high-fare tickets. To implement this parametric model, a decision maker (revenue manager) needs to observe some data to estimate its parameters (buy-up rate and demand distributions), and make decisions (booking limits) using the model. Meanwhile, the choices of booking limits will affect customers' behavior and thus affect the following observed data. We study the above dynamics and show the convergence of booking limits when the buy-up model is misspecified and customer arrivals are actually deterministic. Numerical studies are also provided to show the performance of the model.
Second, we continue the study of the "buy-up" model and consider more complicated actual customers' behavior in which the numbers of different types of customers are stochastic. We present a general necessary condition for the convergence of booking limits and buy-up rate estimates. We provide sufficient conditions for convergence using two different approaches. Comparisons among the optimal revenue, the revenue associated with convergence in the "buy-up" model, and the revenue obtained from the Littlewood rule are presented in the end.
Third, we study the performance of the Littlewood rule when it is used to manage bookings for substitutable fights. We show the convergence of booking limits under some assumptions, and make some conjectures about the limiting behavior of booking limits in other settings. Some numerical studies are performed to enlighten future work.