Joint Product Framing (Display, Ranking, Pricing) and Order Fulfillment Under the Multinomial Logit Model for E-Commerce Retailers
Why this work is in the frame
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Bibliographic record
Abstract
Problem definition: We study a joint product framing and order fulfillment problem with both inventory and cardinality constraints faced by an e-commerce retailer. There is a finite selling horizon and no replenishment opportunity. In each period, the retailer needs to decide how to “frame” (i.e., display, rank, price) each product on his or her website as well as how to fulfill a new demand. Academic/practical relevance: E-commerce retail is known to suffer from thin profit margins. Using the data from a major U.S. retailer, we show that jointly planning product framing and order fulfillment can have a significant impact on online retailers’ profitability. This is a technically challenging problem as it involves both inventory and cardinality constraints. In this paper, we make progress toward resolving this challenge. Methodology: We use techniques such as randomized algorithms and graph-based algorithms to provide a tractable solution heuristic that we analyze through asymptotic analysis. Results: Our proposed randomized heuristic policy is based on the solution of a deterministic approximation to the stochastic control problem. The key challenge is in constructing a randomization scheme that is easy to implement and that guarantees the resulting policy is asymptotically optimal. We propose a novel two-step randomization scheme based on the idea of matrix decomposition and a rescaling argument. Managerial implications: Our numerical tests show that the proposed policy is very close to optimal, can be applied to large-scale problems in practice, and highlights the value of jointly optimizing product framing and order fulfillment decisions. When inventory across the network is imbalanced, the widespread practice of planning product framing without considering its impact on fulfillment can result in high shipping costs, regardless of the fulfillment policy used. Our proposed policy significantly reduces shipping costs by using product framing to manage demand so that it occurs close to the location of the inventory.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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 it