Data-driven distributionally robust capacitated facility location problem
Bibliographic record
Abstract
We study a distributionally robust version of the classical capacitated facility location problem with a distributional ambiguity set defined as a Wasserstein ball around an empirical distribution constructed based on a small data sample. Both single- and two-stage problems are addressed, with customer demands being the uncertain parameter. For the single-stage problem, we provide a direct reformulation into a mixed-integer program. For the two-stage problem, we develop two iterative algorithms, based on column generation, for solving the problem exactly. We also present conservative approximations based on support set relaxation for the single- and two-stage problems, an affine decision rule approximation of the two-stage problem, and a relaxation of the two-stage problem based on support set restriction. Numerical experiments on benchmark instances show that the exact solution algorithms are capable of solving large scale problems efficiently. The different approximation schemes are numerically compared and the performance guarantee of the two-stage problem’s solution on out-of-sample data is analyzed.
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".