SAA-regularized methods for multiproduct price optimization under the pure characteristics demand model

Utility-based choice models are often used to determine a consumer’s purchase decision among a list of available products, to provide an estimate of product demands, and when data on purchase decisions or market shares are available, to infer consumers’ preferences over observed product characteristics. They also serve as a building block in modeling firms’ pricing and assortment optimization problem. We consider a firm’s multi-product pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products considered and the firm’s profit. We then apply a regularized method to compute a solution of the SAA problem and study the convergence of the SAA solutions when the sample size