A data-driven optimization approach for mixed-case palletization and three-dimensional bin packing
Bibliographic record
Abstract
Palletization is the most standard method of packaging and transportation in the retail industry. Their building involves the solution of a three-dimensional packing problem with side practical constraints such as item support and pallet stability, leading to what is known as the mixed-case palletization problem. Motivated by the fact that solving industry-size instances is still very challenging for current methods, we propose a new solution methodology that combines data analysis at the instance level and optimization to build pallets. Item heights are first analyzed to identify possible layers and to derive relationships between item positions. Items are stacked in pairs and trios to create super items, which are then arranged to create layers of even height. The resulting layers are finally stacked to create pallets. The layers are constructed using a reduced-size mixed integer program as well as a two-dimension placement heuristic. Computational tests on industry data show that the solution approach is extremely efficient in producing high-quality solutions in fast computational times.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".