Multi-purchase Behavior: Modeling, Estimation, and Optimization

Problem definition: We study the problem of modeling purchase of multiple products and using it to display optimized recommendations for online retailers and e-commerce platforms. Rich modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the user experience. Methodology/results: We present a parsimonious multi-purchase family of choice models called the BundleMVL-K family and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. We establish the hardness of computing optimal recommendation sets and derive several structural properties of the optimal solution that aid in speeding up computation. This is one of the first attempts at operationalizing multi-purchase class of choice models. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared with competing solutions is shown using several real-world data sets on multiple metrics such as model fitness, expected revenue gains, and run-time reductions. For example, the expected revenue benefit of taking multiple purchases into account is observed to be [Formula: see text] in relative terms for the Ta Feng and UCI shopping data sets compared with the multinomial choice model for instances with ∼1,500 products. Additionally, across six real-world data sets, the test log-likelihood fits of our models are on average 17% better in relative terms. Managerial implications: Our work contributes to the study of multi-purchase decisions, analyzing consumer demand, and the retailers optimization problem. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale, especially in e-commerce platforms and other marketplaces. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2020.0238 .