UCLA

Modeling consumer choice plays a central role in modern business operations and demand prediction. Precedented approaches assume consumers are rational, i.e., assume that consumer choice models follow rational choice theory and are based on the random utility maximization (RUM) principle. However, abundant evidence from marketing science, psychology, and behavioral economics has shown that consumer choice is not always consistent with the RUM assumption.

In this thesis, we introduce a nonparametric and data-driven choice model that is capable of representing any consumer choice, including those that are outside the RUM class. We theoretically characterize the model complexity and propose two practical estimation procedures to learn the model from data. Using real-world transaction data, we demonstrate the out-of-sample prediction ability of the proposed model and extract business insights.

We further transform the proposed model into effective prescriptions. We consider a mixed-integer optimization approach to find the optimal assortment that maximizes expected revenue under the proposed model. We introduce three formulations, analyze the necessary conditions for integrality, and solve them at a large scale by applying Benders decomposition method. Using synthetically generated data, we demonstrate the tractability of our approach and its edge over heuristic approaches from the literature.

Finally, we generalize the estimation procedure of the proposed model as a general solution method for solving large-scale linear optimization problems. The proposed solution method is a randomized algorithm that first samples a set of columns and then solves the linear program that only consists of sampled columns. We theoretically characterize the algorithm's convergence property and apply it to a wide range of applications, including Markov decision processes, covering and packing problems, portfolio optimization, and choice model estimation.