Robust Airline Crew Pairing: Move-up Crews

Due to irregular operations, the crew cost at the end of a month is typically substantially higher than the crew cost projected in planning. We assume that the fleeting and the aircraft routing decisions have already been made. We present a model and a solution methodology that produces robust crew schedules in planning. Besides the objective of minimizing the crew cost, we introduce the objective of maximizing the number of move-up crews, i.e., the crews that can potentially be swapped in operations. To solve the resulting large-scale integer program, we use a combination of delayed column generation and Lagrangian relaxation. The restricted master problem is solved by means of Lagrangian relaxation and the “duals” of the restricted master problem, which are used in delayed column generation, and correspond to the Lagrangian multipliers. We report computational experiments that demonstrate the benefits of using the robust crew schedule instead of the traditional one. We evaluate various crew schedules by generating random disruptions and then running a crew recovery module. We compare solutions with respect to the direct crew cost and indirect costs such as uncovered legs, reserved crews, and deadheading. The main conclusion is that robustness leads to reduced operational crew cost; however, in planning the trade-off between the inflated direct crew cost and robustness needs to be exploited judicially.