A Branch-and-Price-and-Cut Algorithm for the Integrated Scheduling and Rostering Problem of Bus Drivers
Bibliographic record
Abstract
In the transportation industry, crew management is typically decomposed into two phases: crew scheduling and crew rostering. Due to the complexity of scheduling and rostering, bus transportation is not an exception and many relevant studies do not consider both procedures simultaneously. However, such a decomposition can yield inferior schedules/rosters. To address this issue, this paper proposes an integrated scheduling and rostering model for bus drivers and devises a branch-and-price-and-cut (BPC) algorithm to solve the complex problem. The proposed solution framework is empirically applied to real-world instances with various problem sizes whose data is collected from H Bus Company located in southern Taiwan. To validate the effectiveness and evaluate the efficiency of the proposed solution framework, this paper compares the solution obtained from the BPC algorithm with that of a benchmark optimization package. The results show that the proposed BPC algorithm can solve problems with large real-world instances within a reasonable computational time. Moreover, in the numerical experiments, this paper finds that the scheduling and rostering results of the bus drivers are more sensitive to the rostering constraints. Also, the proposed integrated framework can yield a better solution than the solution from a conventional two-phase approach, which demonstrates the advantage of the integration in this paper. The proposed method provided can be employed to deal with the challenges in driver planning for bus companies.
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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 | 0.001 | 0.002 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".