The operational flight and multi-crew scheduling problem

This paper introduces a new kind of operational multi-crew scheduling problem which consists in simultaneously modifying, as necessary, the existing flight departure times and planned individual work day (duties) for the set of crew members, while respecting predefined aircraft itineraries. The splitting of a planned crew is allowed during a day of operations, where it is more important to cover a flight than to keep planned crew members together. The objective is to cover a maximum number of flights from a day of operations while minimizing changes in both the flight schedule and the next-day planned duties for the considered crew members. A new type of the same flight departure time constraints is introduced. They ensure that a flight which belongs to several personalized duties, where the number of duties is equal to the number of crew members assigned to the flight, will have the same departure time in each of these duties. Two variants of the problem are considered. The first variant allows covering of flights by less than the planned number of crew members, while the second one requires covering of flights by a complete crew. The problem is mathematically formulated as an integer nonlinear multi-commodity network flow model with time windows and supplementary constraints. The optimal solution approach is based on Dantzig–Wolfe decomposition/column generation embedded into a branch-and-bound scheme. The resulting computational times on commercial-size problems are very good. Our new simultaneous approach produces solutions whose quality is far better than that of the traditional sequential approach where the flight schedule has been changed first and then input as a fixed data to the crew scheduling problem.