TITLE: Revenue Management with Customer Choice and Sellers Competition

ABSTRACT:

Revenue management is concerned with managing demands of customers and has been found successful in broad areas such as airline, hotel and retailing industries. In revenue management, decisions of sellers such as designing a product portfolio or choosing prices of products are often made based on customer choice. It is thus important to understand customer choice behavior and analyze how it affects sellers' decisions, especially when customers' choice exhibits specific behavioral phenomena that deviate from axioms of rational choice (e.g., Luce's axiom of choice) and sellers compete.

My thesis is focused on revenue management problems, with particular emphasis on customer choice behavior, and it consists of three essential chapters.

In the first chapter, we build a variety of customer booking choice models for a major airline that operates in a very competitive origin-destination market, including the multinomial logit (MNL) models, nested logit (NL) models, mixed-logit (ML) models and latent logit class (LCL) models. The latter three types of models are aimed at incorporating unobserved heterogeneous customer preferences for different departure times of flights and identifying latent customer types. More interestingly, we incorporate in all our models the context effect that the attractiveness of a fare class is influenced by the other fare classes offered in the same assortment, which is not standard in the literature of discrete choice modeling. The estimation results show that including these factors into choice models dramatically affects price sensitivity estimates, and therefore matters.

Previously available algorithms are inefficient for estimating choice models from large sets of data (observations), especially for estimating advanced choice models that usually involve high-dimensional integrals, such as the ML-type models. In the second chapter, we present a stochastic trust region algorithm for ML-type model estimations. The algorithm embeds two sampling processes: (i) a data sampling process and (ii) a Monte Carlo sampling process. The second process is employed to compute the sample average approximation of a high-dimensional integral. The algorithm dynamically controls the sample sizes based on the magnitude of the errors incurred due to the two sampling processes. First, the algorithm controls the size of Monte Carlo samples for each observation in the dataset to minimize the total sample size subject to a constraint on the variance of the objective estimate. Second, the algorithm controls sampling from the dataset according to the magnitude of data sampling error relative to the Monte Carlo sampling error. The first-order convergence (w.p. 1) is proved based on generalized uniform law of large numbers theories for both the objective function and its gradient. The efficiency of the algorithm is tested with data and compared with other algorithms.

In the third chapter, we study how a specific behavioral phenomenon, called the decoy effect, affects the decisions of sellers in product assortment competition in a duopoly. We propose a discrete choice model to capture decoy effects, and we use the model to provide a complete characterization of the Nash equilibria and their dependence on choice model parameters. For the cases in which there are multiple equilibria, we consider dynamical systems models of the sellers responding to their competitors using Cournot adjustment or fictitious play to study the evolution of the assortment competition and the stability of the equilibria. Our results show that all pure-strategy Nash equilibria can provide reliable forecasts of the outcome of the competition in the sense that they have large domains of attraction. In contrast, mixed-strategy Nash equilibria have negligible domains of attraction, except for a special case, and thus we conclude that mixed-strategy Nash equilibria do not provide reliable forecasts of the outcome of the competition. Our results also provide a simple geometric characterization of the dynamics of fictitious play for general $2 \times 2$ games that is more complete than previous characterizations.