Heuristic approaches for flight retiming in an integrated airline scheduling problem of a regional carrier

Flight retiming in airline scheduling consists in slightly modifying the scheduled departure time of some flights with the goal of providing a better service with a cheaper cost. In this research, the departure times must be selected from a small discrete set of options. The whole problem embeds flight retiming, fleet assignment, aircraft routing and crew pairing. Thus, the aim is to determine the departure times of the flights, the fleet assignment and the minimum cost aircraft and crew routes. The objective function takes into account a large cost associated with each crew member, a penalization for short or long connection times, a cost for crew members changing aircraft along their routes, and a minor penalty associated with the use of each aircraft. The constraints enforce aircraft maintenance and crew working rules. In this setting, flight retiming is allowed to potentially reduce the total costs and increase the robustness of the solution against delays by decreasing the number of aircraft changes. We propose and compare four heuristic algorithms based on a Mixed Integer Linear Programming model for the whole problem. The model contains path variables representing the crew pairings, and arc variables representing the aircraft routes. In the heuristic algorithms, column generation is applied on the path variables, and different flight retiming options are considered. The algorithms are tested on real-world instances of a regional carrier flying in the Canary Islands to evaluate their advantages and drawbacks. In particular, one of the algorithms, that uses the solution of the Linear Programming relaxation of the model to select promising options for the departure of the flights, turns out to be the most effective one. The obtained results show that costs can be significantly reduced through flight retiming while still keeping the computing times reasonably short. In addition, we perform a sensitivity analysis by including more retiming options and by using different aircraft and crew costs. Finally, we report the results on larger size instances obtained by combining real-world ones.