A fuzzy multi-objective multi-follower linear Bi-level programming problem to supply chain optimization
Why this work is in the frame
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Bibliographic record
Abstract
In today's world, many planning problems include a hierarchical decision structure with independent and often conflicting objectives. Therefore, the optimization of supply chains with hierarchical structure is essential. In this paper, we investigate a fuzzy multi-objective multi-products supply chain optimization problem in a bi-level structure with one level corresponding to a manufacturer planning problem, while the other to K distribution centers problem. In our model, customer demand and supply chain costs are considered uncertain and will be modeled with use of fuzzy sets. We first describe how different kinds of problems can be modeled as bi-level programming problems. Then, this fuzzy model is first converted into an equivalent crisp model by using -cut method in each level, and then by applying extended Kuhn-Tucker approach, we have a linear multi-objective programming problem. Fuzzy goal programming technique is applied to solve the multi-objective linear programming problem to obtain a set of Pareto-optimal solutions. Finally, a numerical example is illustrated to demonstrate the feasibility of the proposed approach.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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