Data-driven distributionally robust multiproduct pricing problems under pure characteristics demand models

Abstract

This paper considers a multiproduct pricing problem under pure characteristics demand models when the probability distribution of the random parameter in the problem is uncertain. We formulate this problem as a distributionally robust optimization (DRO) problem based on a constructive approach to estimating pure characteristics demand models with pricing by Pang, Su, and Lee. In this model, the consumers’ purchase decision is to maximize their utility. We show that the DRO problem is well-defined, and the objective function is upper semicontinuous by using an equivalent hierarchical form. We also use the data-driven approach to analyze the DRO problem when the ambiguity set, i.e., a set of probability distributions that contains some exact information of the underlying probability distribution, is given by a general moment-based case. We give convergence results as the data size tends to infinity and analyze the quantitative statistical robustness in view of the possible contamination of driven data. Furthermore, we use the Lagrange duality to reformulate the DRO problem as a mathematical program with complementarity constraints, and give a numerical procedure for finding a global solution of the DRO problem under certain specific settings. Finally, we report numerical results that validate the effectiveness and scalability of our approach for the distributionally robust multiproduct pricing problem.