The Vehicle Routing Problem with Time Windows: State-of-the-Art Exact Solution Methods
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Bibliographic record
Abstract
The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to service given customers exactly once each while satisfying the vehicle capacity and customer time windows. The VRPTW has been widely studied. We present here a short survey on the successful exact methods for solving it. These are branch-cut-and-price algorithms, except the most efficient one which solves, by a mixed-integer programming solver, a reduced set partitioning model obtained by performing variable elimination based on reduced cost. This method was able to solve all well-known Solomon's benchmark instances except one, outperforming all the other algorithms previously published. Keywords: vehicle routing; time windows; column generation; branch-cut-and-price; variable elimination by reduced cost
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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 | 0.003 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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