A unifying framework and a mathematical model for the Slab Stack Shuffling Problem
Bibliographic record
Abstract
The Slab Stack Shuffling Problem (SSSP) consists of retrieving slabs, stored in stacks in a warehouse, to efficiently satisfy a processing order. The problem is relevant in the steel industry as the slab yard serves as a storage buffer between the continuous casting stage and the rolling mill. Notably, the SSSP also arises in cutting/assembly centres within the shipbuilding supply chain, where already rolled slabs must undergo further production stages. The different slabs managed in these facilities confer the problem novel practical features, such as the existence of slabs' typologies and deadlines, i.e., a maximum time beyond which their quality certifications expire and are no longer usable. In such a context, the goals of the present paper are twofold: (i) providing a comprehensive taxonomy of the main aspects involved in the problem; (ii) proposing an original mathematical formulation for the SSSP. Specifically, the model is cast as a bi-objective multi-period program, seeking to minimise the number of shuffles and expired slabs. Computational tests on randomly generated instances prove the relevance of the trade-off between the above-mentioned objectives and the impact of the yard's configuration on the retrieval process, suggesting the most suitable storage strategy to adopt under different operational settings.
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".