Coping with uncertainties in production planning through fuzzy mathematical programming: application to steel rolling industry
Bibliographic record
Abstract
This paper adopts the approach of fuzzy set theory into the context of a practical production planning problem encountered frequently in steel rolling mills, where the objective is to establish a cost–minimising master production schedule. To better capture the uncertainties associated with the market demand, the problem is formulated as a fuzzy mixed integer bilinear program (FMIBLP) in which the demand constraints are assumed to be rather flexible and characterised by triangular membership functions. The aspiration level for the decision maker is represented by a linear function where the tolerance limits for this function are determined based on the degree of flexibility in demand that the decision maker is willing to undertake. The fuzzy decision set is obtained using two different types of aggregators which, in turn, allows for the transformation of the fuzzy model into a crisp one seeking the maximum value for the aspiration level. A linearisation scheme is first adopted to transform the bilinear model into an equivalent linear model and then an exterior penalty function based algorithm is employed to the linearised version in order to obtain 'near optimal' solutions that minimise deviations from integral batches. Computational experiments are carried out for different problem instances under both aggregation operators and the results are reported.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".