Joint Optimization of Pricing and Personalized Recommendations in Online Retailing

Abstract

We study the problem of pricing and personalized recommendations in online retailing. A set of products with a fixed starting inventory is offered to different types of customers. The prices can vary over time but need to be consistent across customer groups at all times. Customers' purchase decisions are also influenced by personalized product recommendations. We study a setting where the products are assumed to be independent (i.e., no substitution). However, there is a limit on the number of products that can be recommended to each customer at any given time.

We formulate the problem as a finite-horizon stochastic dynamic program. Due to the constraint on the number of recommended products for each customer, the problem is not separable by product. We propose a solution strategy based on Lagrangian relaxation. We show that the linear programming formulation of the Lagrangian relaxation admits a compact reformulation. Solving the compact reformulation is much more computationally efficient than alternative methods to solve the Lagrangian dual. We further prove a performance guarantee for a heuristic policy based on the solution of the compact reformulation. The policies and bounds are validated with data from a leading online retailer in China. We demonstrate that the proposed policies can achieve significant revenue improvement (over 7%), compared to a policy reflecting the retailer's current practice. We also examine the relative value of personalized recommendations and dynamic pricing; dynamic pricing is shown to be highly valuable, while the value of personalized recommendations is relatively smaller yet still practically significant.

Keywords: Dynamic pricing, personalized recommendation, Lagrangian relaxation, aprroximation algorithms