Operational decisions and learning for multiproduct retail

Abstract

We study multi-product revenue management problems, focusing on the role of uncertainty in both the seller and the customer decision processes. We begin by considering a logit model framework for personalized revenue management problems where utilities are functions of customer attributes, so that data for any one customer can be generalized to others via regression. We establish finite-sample convergence guarantees on the model parameters. The parameter convergence guarantees are then extended to out-of-sample performance guarantees in terms of revenue, in the form of a high-probability bound on the gap between the expected revenue of the best action taken under the estimated parameters and the revenue generated by a decision-maker with full knowledge of the choice model. In the second chapter, we study the static assortment optimization problem under weakly rational choice. This setting applies to most choice models studied and used in practice. We give a mixed-integer linear optimization formulation and present two branch-and-bound algorithms for solving this optimization problem. The formulation and algorithms require only black-box access to purchase probabilities, and thus provide exact solution methods for a general class of discrete choice models, in particular those models without closed-form choice probabilities. We give approximation results for our algorithms in two special cases, and test the performance of our algorithms with heuristic stopping criteria. The third section, motivated by data from an online retailer, describes sales of durable goods online, focusing on the effects of uncertainty about product quality and learning from customer reviews. We describe the nature of the tradeoff between learning product quality over time and substitution effects between products offered in the same category on the same website. Specifically, small differences in product release tines can be magnified substantially over time. The learning process takes longer in markets with more products. The process also takes longer in markets with higher price because customers take more risk in these markets when purchasing under uncertainty. This results in both smaller demand for new products in high-priced markets and more market concentration around fewer, well-established products. We discuss operational implications and show application to a break-even analysis.