A Theoretical Comparison of Feasibility Cuts for the Integrated Aircraft-Routing and Crew-Pairing Problem

The integrated aircraft-routing and crew-pairing problem consists in determining a minimum-cost set of aircraft routes and crew pairings such that each flight leg is covered by one aircraft and one crew, and some side constraints are satisfied. Linking constraints impose minimum connection times for crews that depend on aircraft connections. The main solution approach for this problem consists in solving a constrained crew-pairing problem iteratively, adding feasibility cuts until a solution is found where the connection set used by the crew pairings is feasible for the aircraft-routing problem. The feasibility cuts can be generated by a Benders decomposition approach in which aircraft routing is handled by the subproblem, or they can be selected from a predefined family. We perform a theoretical comparison of the different types of feasibility cuts. We also propose a simple procedure to strengthen these cuts. Computational experiments performed on test instances provided by two major airlines are presented to support the theoretical results.