Ridesharing Problem with Flexible Pickup and Delivery Locations for App-Based Transportation Service: Mathematical Modeling and Decomposition Methods
Bibliographic record
Abstract
App-based transportation service system, such as Uber and Didi, has brought a new transportation mode to users, who are able to make reservations using mobile apps conveniently. However, one of the fundamental challenges in app-based transportation system is the inefficiency and unreliability of the vehicle routing plans caused by complex topology of urban road network and unpredictable traffic conditions. A common way to tackle this problem is repositioning pickup or delivery locations via the coordination between drivers and passengers. This paper studies an on-demand ridesharing problem that determines the optimal ride-share matching strategy and vehicle routing plan with respect to flexible pickup and delivery locations. By introducing the concept of space-time windows, the problem is formulated as the pickup and delivery problem with space-time windows (PDPSW) in space-time network. To solve the model efficiently and accurately, we particularly develop a customized solution approach based on Lagrangian relaxation. Numerical examples are conducted to demonstrate the performance of the proposed framework and draw some managerial insights into the optimal system operation. The results indicate that adopting the serving strategy of flexible pickup and delivery locations will evidently reduce the system cost and improve the service quality in app-based transportation service systems.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".