Traditional models from the revenue management literature assume that firms have full information about the market demand and consumer preferences. This thesis studies pricing, capacity allocation and product line positioning models for a firm with limited market information using relative performance criteria and maximum entropy estimation.
In our first essay, we examine different monopoly pricing mechanisms under limited customer willingness-to-pay (WtP) information. We use the competitive ratio and the maximum regret criteria to study a dynamic pricing, a third-degree price discrimination, and a second-price sealed-bid auction setting, where customers have private WtP drawn from common distribution that is unknown to the seller. We provide closed-form solutions for the optimal pricing policies and highlight important structural insights. We show that price skimming arises naturally as a hedging mechanism against two principal risks that the firm faces: first, the risk of foregoing revenue from pricing too low, and second, the risk of foregoing sales from pricing too high. We focus on the competitive ratio criterion and the dynamic pricing setting to illustrate how learning and partial information can be incorporated. Even limited learning, e.g., market information at a few price points, leads to significant performance gains with relative performance criteria, and the resulting policies have very good revenue performance across all distributions.
In our second essay, we study the joint problem of product line positioning and pricing for a monopolist when consumer preferences and WtP are unknown. We extend classical models of horizontal and vertical differentiation to cover this uncertainty again using the relative performance criteria. Our analysis provides insights into practices observed in many real world markets. For the horizontal differentiation case, we show that the optimal decision for both criteria is to position products at equal intervals in the attribute space and to price them identically. For the vertically differentiated case, we show that the optimal policy consists of offering a number of the highest quality versions, and that the more ambiguity over customers' taste for quality, the more versions the firm should offer.
In our last essay, we change our focus to incorporating partial information in a dynamic forecasting and optimization cycle of capacity allocation.  illustrate, using a two class example, that most common forecasting methods lead to divergence and degeneration of optimal policies when used jointly with optimization routines in such a cycle; and call this phenomenon the "spiral-down effect". We propose a tractable and intuitive approach based on maximum entropy (ME) distributions that readily incorporates and apply uncensoring to censored sales data in an intuitive manner. We show that the protection levels given by our algorithm avoids "spiral down" and converge to optimal values.