Combining Benders’ Decomposition and Column Generation for Integrated Crew Pairing and Personalized Crew Assignment Problems
Bibliographic record
Abstract
The airline crew scheduling problem, because of its size and complexity, is usually solved in two phases: the crew pairing problem and the crew assignment problem. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. The crew pairing problem consists of determining a minimum-cost set of feasible pairings such that each flight is covered exactly once. In the crew assignment problem, the goal is to construct monthly schedules from these pairings for a given set of pilots and copilots independently, while respecting all the safety and collective agreement rules. However, this sequential approach may lead to significantly suboptimal solutions because it does not take into account the crew assignment constraints and objective during the building of the pairings. In this paper, first, we propose an extension of the crew pairing problem that incorporates pilot and copilot vacation requests at the crew pairing stage. Second, we introduce a model that completely integrates the crew pairing and crew assignment problems simultaneously for pilots and copilots. To solve this integrated problem, we develop a method that combines Benders’ decomposition and column generation. We conduct computational experiments with real-world data from a major U.S. carrier.
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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 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| 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 | 0.001 |
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".