Pricing with Consumer Sequential Choice Model and Its Application in the Design of a Threshold-Type Promotion

A threshold-type promotion is to discount items by a flat dollar amount when a consumer’s total consumption level exceeds a given threshold. The goal of this paper is to understand the effect of the promotion on companies’ sales and profit and propose a data-driven approach to jointly price items and optimize the promotion decisions. We propose a novel sequential choice model to characterize a consumer’s choice of multiple items in a single transaction. The sequential choice model generalizes the traditional choice model, which assumes at most one item chosen in one transaction. Based on that, we establish a general convex pricing optimization framework under mild conditions. We further show that the threshold-type promotion problem fits in the framework with an extra set of pricing constraints. Finally, we provide a data-driven approach based on the proposed pricing model to solve a joint pricing and promotion design problem. Under the assumption of exponential marginals, we estimate the choice model from sales data by a linear program and obtain the optimal price and promotion by solving a mixed-integer linear program. Finally, several numerical studies are conducted to test the efficiency of the framework and understand the effect of promotion on companies’ profit.