Pricing and Assortment Optimization Under Logit‐Based Choice Models With Tree‐Structured Consideration Sets
Bibliographic record
Abstract
ABSTRACT We study pricing and assortment optimization problems under logit‐based choice models with two tree‐structured consideration sets, that is, the subtree structure and the induced paths structure. In each model, there are multiple customer types, and each customer type is a combination of the product preference vector and the consideration set. A customer of a particular type only purchases products within his consideration set. The tree structure means all products form a tree with each node representing one product, and all consideration sets are induced from this tree. In the subtree structure, each consideration set consists of products in a subtree, and in the induced paths structure, each consideration set consists of products on the path from one node to the root. Customers make purchase decisions following the mixed multinomial logit model (MMNL) or the multilevel nested logit model (multilevel NL). The goal of the pricing and assortment optimization is to determine a set of products offered to customers along with the prices such that the expected revenue is maximized. We consider both the unconstrained problem and the capacitated problem. We propose a unified framework, which captures the tree structure, to design fully polynomial time approximation schemes (FPTAS) for all these problems.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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".