Branch-Price-and-Cut for the Electric Vehicle Routing Problem with Heterogeneous Recharging Technologies and Nonlinear Recharging Functions
Bibliographic record
Abstract
As electric vehicles become increasingly prevalent, effective planning of their use becomes paramount. The electric vehicle routing problem, characterized by limited driving range and the need for recharging, poses unique challenges compared with traditional vehicle routing problems. This paper proposes a branch-price-and-cut solution method tailored for the electric vehicle routing problem with time windows, heterogeneous recharging technologies, and nonlinear charging functions (E-VRPTW-NL). The methodology differs from previous methods proposed in the literature by handling nonlinear recharging functions in the pricing problem. The pricing problem is solved by a bidirectional labeling algorithm that efficiently handles the complex interdependency between time and state of charge during recharge scheduling. The proposed solution method is tested on both benchmark instances from the literature as well as new instances. Tests show that the solution method is competitive with well-known solution methods from the literature on simpler variants of the problem. The computational results also indicate that the proposed method can solve new E-VRPTW-NL instances with up to 100 customers and 21 recharge locations within one hour. Further analysis explores how simplifying the modeling of the recharging process affects solution feasibility and cost. The results show that keeping the heterogeneity of the recharging functions is crucial, whereas simplifying the shape of each recharging function has limited impact. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0725 .
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 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".