Multi-Purchase Behavior: Modeling and Optimization

40 Pages Posted: 8 Jul 2020

See all articles by Theja Tulabandhula

Theja Tulabandhula

University of Illinois at Chicago

Deeksha Sinha

Massachusetts Institute of Technology (MIT)

Prasoon Patidar

Carnegie Mellon University

Date Written: February 26, 2020


We study the problem of modeling purchase of multiple items and utilizing it to display optimized recommendations, which is a central problem for online e-commerce platforms. Rich personalized modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the end user experience. 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. This is one of the first attempts at operationalizing multi-purchase class of choice models. We characterize structural properties of the optimal solution, which allow one to decide if a product is part of the optimal assortment in constant time, reducing the size of the instance that needs to be solved computationally. We also establish the hardness of computing optimal recommendation sets. 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 to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. The benefit of taking multiple purchases into account is observed to be $6-8\%$ in relative terms for the Ta Feng and UCI shopping datasets when compared to the MNL model for instances with $\sim 1500$ products. Additionally, across $8$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms.

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.

Keywords: Multi-choice purchase behavior, recommendations, scalable algorithms, structural properties

Suggested Citation

Tulabandhula, Theja and Sinha, Deeksha and Patidar, Prasoon, Multi-Purchase Behavior: Modeling and Optimization (February 26, 2020). Available at SSRN: or

Theja Tulabandhula (Contact Author)

University of Illinois at Chicago ( email )

1200 W Harrison St
Chicago, IL 60607
United States

Deeksha Sinha

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Prasoon Patidar

Carnegie Mellon University ( email )

Pittsburgh, PA 15213-3890
United States

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