Second-order cone programming approach to common set of weights in multiplicative network DEA model
Bibliographic record
Abstract
Data Envelopment Analysis (DEA) is a data-driven approach employed to evaluate the efficiency of Decision-Making Units (DMUs). While DEA enables DMUs to determine the most favorable set of weights for optimizing their efficiency scores, this flexibility hinders direct comparison across all DMUs due to the absence of a common weighting scheme. This research proposes a model for analyzing Network DEA in multiplicative form and introduces a programming model aimed at finding a Common Set of Weights (CSW) that maximizes the efficiency of each stage concurrently. The proposed CSW model for multiplicative Network DEA is non-linear but can be converted into a Second-Order Cone Programming (SOCP) problem, a well-established convex optimization method capable of efficiently finding optimal solutions. This study disaggregates system efficiency into the product of efficiencies across each network stage, extends the analysis to include system-oriented, stage-oriented, and process-oriented cases. The rationality and robustness of the proposed model are validated through Monte Carlo simulation experiments and empirical two-stage dataset, further confirming its advantages in hierarchical discrimination and robustness.
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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 | 0.005 |
| 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 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".