A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture

The airline’s ability to offer flight schedules that provide service to passengers at desired times in competitive markets, while matching demand with an aircraft fleet of suitable size and composition, can significantly impact its profits. In this spirit, optional flight legs can be considered to construct a profitable schedule by optimally selecting among such alternatives in concert with assigning the available aircraft fleet to all the scheduled legs. Examining itinerary-based demands as well as multiple fare-classes can effectively capture network effects and realistic demand patterns. In addition, allowing flexibility on the departure times of scheduled flight legs can increase connection opportunities for passengers, hence yielding robust schedules while saving fleet assignment costs within the framework of an integrated model. Airlines can also capture an adequate market share by balancing flight schedules throughout the day, and recapture considerations can contribute to more realistic accepted demand realizations. We therefore propose in this paper a model that integrates the schedule design and fleet assignment processes while considering flexible flight times, schedule balance, and recapture issues, along with optional legs, path/itinerary-based demands, and multiple fare-classes. A polyhedral analysis is conducted to generate several classes of valid inequalities, which are used along with suitable separation routines to tighten the model representation. Solution approaches are designed by applying Benders decomposition method to the resulting tightened model, and computational results are presented using real data obtained from United Airlines to demonstrate the efficacy of the proposed procedures.