We study the problem of modeling purchase of multiple products and utilizing it to display optimized recommendations for online retailers and e-commerce platforms. We present a parsimonious multi-purchase family of choice models called the Bundle-MVL-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 to competing solutions is shown using several real world datasets 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 $\sim5\%$ 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 $6$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms. Our work contributes to the study 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.

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