A bilinear programming model and a modified branch-and-bound algorithm for production planning in steel rolling mills with substitutable demand
Bibliographic record
Abstract
In this paper, we address an instance of the dynamic capacitated multi-item lot-sizing problem (CMILSP) typically encountered in steel rolling mills. Production planning is carried out at the master production schedule level, where the various end items lot sizes are determined such that the total cost is minimised. Through incorporating the various technological constraints associated with the manufacturing process, the integrated production–inventory problem is formulated as a mixed integer bilinear program (MIBLP). Typically, such class of mathematical models is solved via linearisation techniques which transform the model to an equivalent MILP (mixed integer linear program) at the expense of increased model dimensionality. This paper presents an alternative branch-and-bound based algorithm that exploits the special structure of the mathematical model to minimise the number of branches and obtain the bound at each node. The performance of our algorithm is benchmarked against that of a classical linearisation technique for several problem instances and the obtained results are reported.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".