A Representative Consumer Model in Data-Driven Multi-Product Pricing Optimization

In this paper, we develop a data-driven approach to recover the “right” choice model for the multi-product pricing problem, using the theory of a representative consumer in discrete choice. This approach uses a regularization function to capture diversification in choice behaviour, and establishes a set of closed-form relationships between the prices and choice probabilities with a separable function. By penalizing against deviation from these relationships in the data set, we propose a new loss function that is used to derive efficient algorithms for the inverse optimization problem, in both online and offline settings. This allows us to use second-order cone and linear programs to estimate the representative consumer model. Mixed-integer linear programming is used to find the optimal prices when side constraints are present, else the pricing problem reduces to solving a linear program. Extensive tests using both synthetic and industry data demonstrate clearly the benefits of this approach