Assortment Optimization with α-Similar Substitutes: Insights from Customer Browsing Patterns
Bibliographic record
Abstract
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 [Formula: see text]-similar substitutes property, which requires that all customers have consideration sets that lie in intervals (in the sorting) of length at most [Formula: see text], where [Formula: see text] 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 [Formula: see text]. Moreover, we show that the assortment optimization for some specific choice model with [Formula: see text]-similar substitutes property is polynomial-time solvable. We demonstrate our approach—going from data to modeling (i.e., selecting an appropriate [Formula: see text]) 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 [Formula: see text]-similar substitutes property in the presence of customers with large consideration sets. We provide an approximation guarantee in terms of revenue when asserting the [Formula: see text]-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 .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".