Branch-and-Price–Based Algorithms for the Two-Echelon Vehicle Routing Problem with Time Windows
Bibliographic record
Abstract
This paper studies the two-echelon capacitated vehicle routing problem with time windows. The first echelon consists of transferring freight from depots to intermediate facilities (i.e., satellites), whereas the second echelon consists of transferring freight from these facilities to the final customers, within their time windows. We propose two path-based mathematical formulations for our problem: (1) in one formulation, paths are defined over both first- and second-echelon tours, and (2) in the other one, the first- and second-echelon paths are decomposed. Branch-and-price–based algorithms are developed for both formulations. We compare both formulations and solution methods on a comprehensive set of instances and are able to solve instances up to five satellites and 100 customers to optimality. This paper is the first paper in the literature that solves such large instance sizes. The online appendix is available at https://doi.org/10.1287/trsc.2018.0844 .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".