The Robust Vehicle Routing Problem with Time Window Assignments
Bibliographic record
Abstract
In practice, there are several applications in which logistics service providers determine the service time windows at the customers, for example, in parcel delivery, retail, and repair services. These companies face uncertain travel times and service times that have to be taken into account when determining the time windows and routes prior to departure. The objective of the proposed robust vehicle routing problem with time window assignments (RVRP-TWA) is to simultaneously determine routes and time window assignments such that the expected travel time and the risk of violating the time windows are minimized. We assume that the travel time probability distributions are not completely known but that some statistics, such as the mean, minimum, and maximum, can be estimated. We extend the robust framework based on the requirements’ violation index, which was originally developed for the case where the specific requirements (time windows) are given as inputs, to the case where they are also part of the decisions. The subproblem of finding the optimal time window assignment for the customers in a given route is shown to be convex, and the subgradients can be derived. The RVRP-TWA is solved by iteratively generating subgradient cuts from the subproblem that are added in a branch-and-cut fashion. Experiments address the performance of the proposed solution approach and examine the trade-off between expected travel time and risk of violating the time windows.
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".