Parametric analysis of objective function coefficients and right-hand-side parameters of linear programming models across the entire feasible range
Bibliographic record
Abstract
Management decisions today can be supported by a large amount of data.To enable the effective use of the data, proper mathematical models are required, which can help one explore patterns that are useful for decision makers.If linear programming (LP) and related sensitivity analysis take advantage of increased computational power and the extended possibilities of informatics, then LP models might usefully serve as tools for data analytic.This paper demonstrates how parametric analysis for the entire feasible region of a right-hand side parameter or an objective function coefficient can be performed.Parameterised LPs are defined for the calculations, and techniques for speeding up the calculations are recommended.The proposed method is implemented in an AIMMS environment and illustrated with a production planning problem.The required computation time for the calculation is also analysed with the help of several size benchmark LP models.The extended LP sensitivity information presented in this paper clarifies the consequences of parameter changes and may lead to better management decisions whenever scarce resources must be allocated to alternatives and LP models are applied.
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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 | 0.004 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".