Optimizing Revenue over Data-driven Assortments

TL;DR

This paper introduces scalable algorithms for large-scale assortment optimization under the multinomial logit model, enabling real-time personalized recommendations in e-commerce with millions of items.

Contribution

It proposes novel binary search-based algorithms with vector space embeddings that significantly improve computational efficiency for arbitrary assortment collections.

Findings

Algorithms operate in sub-linear time for large assortment collections.

Empirical results demonstrate effectiveness on datasets with up to 100,000 items.

Methods outperform existing approaches in speed and scalability.

Abstract

We revisit the problem of large-scale assortment optimization under the multinomial logit choice model without any assumptions on the structure of the feasible assortments. Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment choices to be made, not imposing any constraints on the collection of feasible assortments gives more flexibility to incorporate insights of store-managers and historically well-performing assortments. We design fast and flexible algorithms based on variations of binary search that find the revenue of the (approximately) optimal assortment. We speed up the comparisons steps using novel vector space embeddings, based on advances in the information retrieval literature. For an arbitrary collection of assortments, our algorithms can find a solution in time that is sub-linear in the number of assortments and for the simpler case of cardinality constraints - linear in the number of items (existing methods are quadratic or worse). Empirical validations using the Billion Prices dataset and several retail transaction datasets show that our algorithms are competitive even when the number of items is $\sim 10^5$ ($100$x larger instances than previously studied).