Customer-driven Bundle Promotion Optimization at Scale

Abstract

Bundle promotions have become increasingly popular among online retailers due to their potential in increasing revenue and profit. They take various forms depending on how retailers structure them and offer them to customers. Understanding how customers respond to these promotions and designing optimal bundle promotions at scale are relevant but challenging problems due to their nonlinear nature. We study a new class of bundle promotions that are not advertised but are offered during customers need based shopping (product consideration) process on a retailer's website. In our problem, we determine a subset of products, namely a bundle set. If a customer considers a product from the bundle set during her shopping journey, she is offered the bundle promotion, either through Buy x Get y promotions or at checkout. If she adds another product from the bundle set to her basket, she receives the bundle discount. We introduce a conditional customer-choice framework and a mathematical model to determine an optimal bundle set. The problem is a large-scale binary nonlinear program, and we prove it is APX-hard. We identify a coefficient indicating each product's revenue potential if included in the bundle set. We design approximation methods by applying various techniques to approximate the products' revenue potentials. We present theoretical analyses and error bounds for our approximation methods and numerically verify their excellent performance. We find that connectivity of product graphs and the strength of the product interactions are the main factors that drive the magnitude of the revenue improvement.

Keywords: Bundle promotion, customer-driven bundles, large-scale optimization, design and analysis of algorithms, approximation methods.