Congratulations to Jun Han on earning his doctorate!

Abstract: In order to extract maximum surplus from a heterogeneous customer base it is common practice for firms to offer a portfolio of differentiated products, from which consumers of different preferences can select their favorite items. The standard model of product line design heavily relies on the distribution of consumers’ willingness-to-pay, while such information can be rather inaccurate with estimation error and biased data. This thesis aims to address this problem through robust optimization and consists of three main chapters. In the first chapter we consider product line design in the case of the unknown probability of consumer types or with some prior knowledge of its bound. Based on a classic two-type model with a new set of less restrictive assumptions, we analyze properties of the optimal menu. We maximize a performance index to obtain the optimal robust solution, equivalent to the robustness criterion of minimax relative regret. For a popular parametrization of utility and cost functions, the optimal performance index is not smaller than 75% regardless of any possible consumer distribution with known type values. In the second chapter, we examine a product line model with an arbitrary number of consumer types and products in a generalized setting. Accounting for the uncertainty of both consumer types and their probabilities, our optimal robust product line has positive qualities across all products. It is remarkable that without knowing the exact number of consumer types the firm can achieve the optimal robust performance. We also study robust solutions under two other commonly used robustness criteria, including maximin payoff and minimax absolute regret. We demonstrate the effect of product variety on robust product lines and a menu-cost-adjusted performance index is proposed in order to decide how many products to provide robustly. As an alternative, data-driven distributionally robust optimization can be leveraged to determine a product line. Finally, in the third chapter, a novel optimization model is introduced for product line design given functions of utility, variable and fixed cost, and the number of products offered is endogenously determined. For robust pricing of some fixed products, we propose two methods to account for uncertainty of the willingness-to-pay distribution: one follows from a classic paradigm of robust optimization, and the other employs distributionally robust optimization with a Wasserstein distance characterizing data imprecision. Forboth methods, the optimization problems to offer the robust product lines are equivalent to mixed-integer linear programs.