Assortment Optimization with $\alpha$-Similar Substitutes: Insights from Customer Browsing Patterns

We propose an approach to model assortment optimization problems based on two observations we made from customer browsing history on Taobao. First, most customers consider very few items (no more than five) before purchasing. Second, there exists a sorting of items so that most customer consideration sets are contained in small intervals in this sorting. This sorting can be discovered by the Cuthill-McKee algorithm, which is designed to work with sparse matrices. We encode these two observations into the $\alpha$-similar substitutes property, which requires that all customers have consideration sets that lie in intervals (in the sorting) of length at most $\alpha$, where $\alpha$ is a parameter we select and is fitted from data. The assortment optimization and pricing problems associated with this property are fixed-parameter tractable for a fixed $\alpha$. Moreover, we show that the assortment optimization for some specific choice model with $\alpha$-similar substitutes property is polynomial-time solvable. We demonstrate our approach—going from data to modeling (i.e., selecting an appropriate $\alpha$) and finally to optimization—on another data set of customer click history on JD.com. Lastly, we conduct sensitivity tests on choice models that satisfy the $\alpha$-similar substitutes property in the presence of customers with large consideration sets. We provide an approximation guarantee in terms of revenue when asserting the $\alpha$-similar substitutes property. Both theoretical and numerical results show that the optimal assortment of our estimated model captures most of the revenue even when there are customers with large consideration sets.

This paper was accepted by Vivek Farias, data science.

Funding: B. Jiang’s research is supported by the National Natural Science Foundation of China [Grants 72394364, 72394363, 72394360, 72171141, and 72442013]. C. T. Ryan is supported by the NSERC [Grant RGPIN-2020-06488] and the SSHRC [Grant AWD-029333]. N. Zhang is supported by Ivey Business School.

Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2023.00786.