A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times
Bibliographic record
Abstract
The vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST) introduced by Errico et al. (2013) in the form of a chance-constrained model mainly differs from other vehicle routing problems with stochastic service or travel times considered in the literature by the presence of hard time windows. This makes the problem extremely challenging. In this paper, we model the VRPTW-ST as a two-stage stochastic program and define two recourse policies to recover operations feasibility when the first stage plan turns out to be infeasible. We formulate the VRPTW-ST as a set partitioning problem and solve it by exact branch-cut-and-price algorithms. Specifically, we developed efficient labeling algorithms by suitably choosing label components, determining extension functions, and developing lower and upper bounds on partial route reduced cost to be used in the column generation step. Results on benchmark data show that our methods are able to solve instances with up to 50 customers for both recourse policies.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".