A Scheduling-based Constraint Programming Approach to Solving a Complex Two-dimensional Two-stage Cutting Stock Problem
Bibliographic record
Abstract
We investigate the novel Two-Dimensional Two-stage Cutting Stock Problem with Flexible Length, Flexible Demand, Order-to-Order Marriageability, and Scheduling Costs (2SCSP-FFMS): orders for rectangular items must be cut from treated rectangular stocks using guillotine cuts with the objective to minimize waste, inventory cost, and tardiness cost. Different from problems in the literature, the 2SCSP-FFMS allows the item length and total order demands to vary within customer-specified intervals. We first investigate a variation of the problem that ignores marriageability (pairwise conflicts between orders) and scheduling costs, proposing constraint programming models, mixed-integer programming models, and heuristics. Then, we study a second variation that adds the marriageability requirement before examining the full 2SCSP-FFMS problem. Accordingly, we extend the approaches that performed best in the first variation to the second one and the full 2SCSP-FFMS. For each of these problems, we perform empirical analysis on both generated and real-life industrial instances. Notably, our scheduling-based constraint programming model has orders-of-magnitude smaller memory requirements over other exact methods and can be competitive with a customized multi-phase heuristic.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".