Mixed integer linear programming model for a multi-depot arc routing problem with different arc types and flexible assignment of end depot
Bibliographic record
Abstract
This article addresses a street sweeping problem that extends the class of multi-depot arc routing problem by integrating a flexible assignment of end depot for each working shift. A unique team of specialized vehicles starts each shift from a depot, visits the required arcs and returns at the end of each shift to a depot. The service in the next shift should start from the end depot of the previous one. An additional new constraint imposes that the highway arcs must be serviced during a night shift while all others arcs (boulevard, street, etc.) can be swept during both day and night. The aim of this arc routing problem is to find optimal shifts that satisfy these two practical aspects, along with other constraints such as maximum shift duration. The problem is motivated by a real-world application that has not been previously studied in the literature. A mixed integer linear programming model is formulated with the objective of minimizing the total travel time and tested on newly generated instances based on Cordeau's multi-depot vehicle routing problem instances. The results show a generation of total travel time savings up to 12 % compared to the single depot arc routing problem.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".