The Uncapacitated Facility Location Problem with Client Matching
Bibliographic record
Abstract
The Uncapacitated Facility Location Problem with Client Matching (LCM) is an extension of the Uncapacitated Facility Location Problem (UFLP), where two clients allocated to a facility can be matched. As in the UFLP, facilities can be opened at any of m predefined locations with given fixed costs, and n clients have to be allocated to the open facilities. In classical location models, the allocation cost is the distance between a client and an open facility. In the LCM, the allocation cost is either the cost of a return trip between the facility and the client, or the length of a tour containing the facility and two clients. The similarities of the LCM with the classical UFLP and the matching problem are exploited to derive valid inequalities, optimality cuts, and polyhedral results. A greedy heuristic and a branch-and-cut algorithm are developed, and several separation procedures are described. Computational experiments confirm the efficiency of the proposed approach.
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.005 |
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; both teacher heads agree on what is shown here.
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".