Exact Approaches for Designing Multifacility Buy-at-Bulk Networks
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Bibliographic record
Abstract
We study a problem that integrates buy-at-bulk network design into the classical facility location problem. We consider a generalization of the facility location problem where multiple clients may share a capacitated network to connect to open facilities instead of requiring direct links. In this problem, we wish to open facilities, build a routing network by installing access cables of different costs and capacities, and route every client demand to an open facility. We provide a path-based formulation and we compare it with the natural compact formulation for this problem. We then design an exact branch-price-and-cut algorithm for solving the path-based formulation. We study the effect of two families of valid inequalities. In addition to this, we present three different types of primal heuristics and employ a hybrid approach to effectively combine these heuristics in order to improve the primal bounds. We finally report the results of our approach that were tested on a set of real world instances, as well as two sets of benchmark instances and evaluate the effects of our valid inequalities and primal heuristics.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 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