Price Optimization Under the Mixture of Boundary Logit Model

Abstract

We study price optimization under the mixture of boundary logit (MBL) model, which was recently introduced in Jagabathula et al. (2020) and Jagabathula and Venkataraman (2022). The model belongs to the consider-then-choose class of choice models and generalizes the rank-based model by addressing its two major limitations: it incorporates the dependency of customer preferences on product features and captures indifferent preferences between two or more products. We show that the pricing problem under the MBL model is hard to solve in the most general case. However, we prove structural results for the general pricing problem and characterize the optimal solution for several special cases, including a setting in which all products are charged the same price, and a setting with two products. Motivated by our structural results, we show that the general pricing problem can be formulated as a mixed integer linear program (MILP) and thus tackled with state-of-the-art integer programming solvers. Finally, we propose efficient heuristics for solving the pricing problem and evaluate their performance relative to the optimal pricing policy using extensive numerical experiments. The MBL model and the proposed MILP formulation provide a tractable framework for price optimization in an online retail setting where customers first form a consideration set and then make a purchase decision. Moreover, the proposed heuristics provide competitive alternatives in terms of obtained revenue and computational effort for instances with a larger number of customers and/or products.

Keywords: Choice Models, Consideration Set, Pricing, Online Retail