A Data-Driven Approach to Modeling Assortment Optimization : The Tractable Case of Similar Substitutes

We propose a data-driven approach to model assortment optimization problems based on three real data sets. Our work is motivated by two empirical observations from customers browsing history on Taobao: one is that most customers browse very few items (<=5) before they make a purchase; the second is that there exists a sorting of items so that customer consideration sets are a small interval in the sorting. This algorithm sorting can be discovered by an algorithm due to Cuthill and McKee (1969). Based on these empirical observations, we build a framework for choice models, and show the connection between our framework and some popular choice models. To verify that models under our framework capture reality well, we use the dataset from Bodea et al. to fit different models and compare their performance on out-of-sample data. The result shows that our model provides a good balance between prediction accuracy and model complexity. Then, we consider the assortment optimization and pricing problem under our model and give fixed-parameter tractable algorithms for both problems. Finally, we implement our approach - going from data to modeling, and finally to optimization - on a third data set of customer clicking history on JD.com