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 .
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".