Multi-objective mixed integer programming modelling for closed-loop supply chain network design: an enhanced Benders decomposition algorithm
Why this work is in the frame
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Bibliographic record
Abstract
Considering a closed-loop supply chain (CLSC) network with uncertain demand and recycling rates, this article innovatively designs a multi-objective mixed-integer programming model that incorporates corporate social responsibility (CSR), a facility retrofit strategy (FRS), a flexible supply strategy (FSS) and a vehicle selection strategy (VSS). Then, robust optimization methods are applied to construct robust models under three situations of uncertainty. For the computational complexity of large-scale problems, an enhanced Benders decomposition algorithm (EBDA) is designed. A numerical case analysis is conducted using five different scale instances. First, compared to other algorithms, EBDA accelerates the solution efficiency while ensuring convergence. Secondly, the sensitivity of the objective weights and the trade-offs of multiple objectives are analysed. Finally, the impact is analysed of the uncertain environment, CSR, an FRS, an FSS and a VSS on the CLSC network. Decision makers need to balance three objectives to manage CLSC and use these strategies appropriately to address the negative impact of an uncertain environment.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| 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 it