Pricing And Assortment Problems Under Correlated Product Evaluations
In many retail settings, demand for a certain product is determined not only by its own attributes but also by the attributes of other products, creating interactions among the demands for different products. This thesis focuses on settings where a retailer offers heterogeneous products that can be designated into a number of different subgroups such that product evaluations, i.e., the utilities that a customer assigns to products within a subgroup, are correlated. We focus on positive correlation among product evaluations within subgroups, meaning that products within a subgroup are closer substitutes to each other than products from another subgroup. We use the Nested Logit (NL) model as a tool to capture correlated product evaluations. In the Nested Logit model, a customer follows a two-stage choice process where she first selects a product subgroup, followed by a specific product within that group. The first part of the thesis focuses on a pricing problem where a firm offers a product for sales through several distinct sales channels and the utility derived from purchasing the product in each channel depends on its price. In each sales channel, there are also competing products not under our firm's control which must be taken into consideration. We provide sequential methods for obtaining maximizers of the revenue function and provide structural properties pertaining to the markups on optimal prices. The second part of the thesis focuses on pricing problems in which the prices of offered products are subject to bound constraints and the utility derived from each product depends on its price. We give approximation methods that allow the user to specify a performance guarantee a priori, where the final solutions are obtained by solving linear programs whose sizes scale gracefully with the specified performance guarantee. In addition, we develop a linear program that we can use to quickly obtain upper bounds on optimal expected revenues. The final part of the thesis focuses on an assortment offering problem in which operational costs are incorporated in the form of inventory considerations. We provide theoretical and numerical results concerning the effect of correlation between product evaluations within a subgroup on optimal assortment sizes, optimal profits and optimal stocking levels. We give structural properties of optimal assortments within each subgroup, and provide efficient dynamic-programming based solution approaches for finding near-optimal assortments.
Todd, Michael Jeremy; Henderson, Shane G.
Ph. D., Operations Research
Doctor of Philosophy
dissertation or thesis