Fair Stochastic Vehicle Routing with Partial Deliveries
Bibliographic record
Abstract
This paper explores the fair stochastic vehicle routing problem with partial deliveries (FSVRP-PD), a variant of the traditional vehicle routing problem with uncertain customer demands. Unlike conventional approaches that mandate full customer demand satisfaction, we relax this requirement to accommodate several real-world applications, such as humanitarian logistics and food rescue operations, where total demand often exceeds available resources. Our proposed solution approach promotes fair and equitable distribution of resources across all beneficiaries by requiring that the expected fill rate for each customer meets a predefined threshold. A solution to the FSVRP-PD constitutes a set of routes with a minimal total routing cost, where the expected minimum fill rates are met for every customer. Finding such a solution requires solving two interdependent subproblems: route planning and sequential resource allocation. To this extent, we develop an exact branch-price-and-cut algorithm capable of solving instances with up to 75 customers. Resource allocation follows Rawlsian fairness criteria that maximize the minimum service level across all customers in a route. To enhance the performance of the algorithms, particularly in pricing problems, we propose several problem-specific bounding techniques. Through numerical experiments, we demonstrate that our approach outperforms traditional routing and resource allocation policies by yielding superior cost and service equity outcomes. Funding: This work was funded by the Dutch Research Council (NWO) DAta-dRiven E-Commerce Order FULfillment (DAREFUL) Project [Grant 629.002.211]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0556 .
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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 | 0.006 |
| 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 | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".