Click-Based MNL: Algorithmic Frameworks for Modeling Click Data in Assortment Optimization

Abstract

In this paper, we introduce the click-based MNL choice model, a novel framework for capturing customer purchasing decisions in e-commerce settings. Our main modeling idea is to assume that the click behavior within product recommendation or search results pages provides an exact signal regarding the alternatives considered by each customer. We study the resulting assortment optimization problem, where the objective is to select a subset of products, made available for purchase, to maximize the expected revenue. Our main algorithmic contribution comes in the form of a polynomial-time approximation scheme (PTAS) for this problem, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. In the course of establishing this result, we develop novel technical ideas, including enumeration schemes and stochastic inequalities, which may be of broader interest. In order to quantify the benefits of incorporating click behavior within choice models, we present a case study based on data acquired in collaboration with the retail giant Alibaba. We fit click-based MNL and standard MNL models to historical sales and click data in a setting where the online platform must present customized six-product displays to users. We demonstrate that utilizing the click-based MNL model leads to substantial improvements over the standard MNL model in terms of prediction accuracy. Furthermore, we generate realistic assortment optimization instances that mirror Alibaba's customization problem, and implement practical variants of our approximation scheme to compute assortment recommendations in these settings. We find that the recommended assortments have the potential to be at least 9% more profitable than those resulting from a standard MNL model. We identify a simple greedy heuristic, which can be implemented at large scale, while also achieving near-optimal revenue performance in our experiments.