Online Learning and Optimization for Revenue Management Problems with Add-on Discounts

We study in this paper a revenue management problem with add-on discounts. The problem is motivated by the practice in the video game industry, where a retailer offers discounts on selected supportive products (e.g. video games) to customers who have also purchased the core products (e.g. video game consoles). We formulate this problem as an optimization problem to determine the prices of different products and the selection of products with add-on discounts. To overcome the computational challenge of this optimization problem, we propose an efficient FPTAS algorithm that can solve the problem approximately to any desired accuracy. Moreover, we consider the revenue management problem in the setting where the retailer has no prior knowledge of the demand functions of different products. To resolve this problem, we propose a UCB-based learning algorithm that uses the FPTAS optimization algorithm as a subroutine. We show that our learning algorithm can converge to the optimal algorithm that has access to the true demand functions, and we prove that the convergence rate is tight up to a certain logarithmic term. In addition, we conduct numerical experiments with the real-world transaction data we collect from a popular video gaming brand's online store on Tmall.com. The experiment results illustrate our learning algorithm's robust performance and fast convergence in various scenarios. We also compare our algorithm with the optimal policy that does not use any add-on discount, and the results show the advantages of using the add-on discount strategy in practice.