Workload equity in multiperiod vehicle routing problems
Bibliographic record
Abstract
Abstract An equitable distribution of workload is essential when deploying vehicle routing solutions in practice. For this reason, previous studies have formulated vehicle routing problems with workload‐balance objectives or constraints, leading to trade‐off solutions between routing costs and workload equity. These methods consider a single planning period; however, in practice, equity is often sought over several days. In this work, we show that workload equity over multiple periods can be achieved without impact on transportation costs when the planning horizon is sufficiently large. This is demonstrated in the context of a generic multiperiod vehicle routing problem, using a simple two‐phase method. In the first phase, solutions of minimal distance are produced for each period. Next, the resulting routes are allocated to drivers to obtain equitable workloads over the planning horizon. We conducted extensive numerical experiments to measure the performance of the proposed approach and the level of workload equity achieved for different planning‐horizon lengths. For horizons of five days or more, we observed that quasi‐optimal workload equity and optimal routing costs can be jointly achievable.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".