Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information
Bibliographic record
Abstract
Accurately estimating the length of Vehicle Routing Problem (VRP) distances can inform transportation planning in a wide variety of delivery and service provision contexts. This study extends the work of previous research where multiple linear regression models were used to estimate the average distance of VRP solutions with various customer demands and capacity constraints. This research expands on that approach in two ways: first, the point patterns used in estimation have a wider range of customer clustering or dispersion values as measured by the Average Nearest Neighbor Index (ANNI) as opposed to just using a Poisson or random point process; second, the tour coefficient adjusted by this complementary spatial information is shown to exhibit statistically more accurate estimations. To generate a full range of ANNI values, point patterns were simulated using a Poisson process, a Matern clustering process, and a simple sequential inhibition process to obtain random, clustered, and dispersed point patterns, respectively. The coefficients of independent variables in the models were used to explain how the spatial distributions of customers influence the VRP distances. These results demonstrate that complementary spatial data can be used to improve operational results, a concept that could be applied more broadly.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".