A Robust Pairing Model for Airline Crew Scheduling

Delays and disruptions in airline operations annually result in billions of dollars of additional costs to airlines, passengers, and the economy. Airlines strive to mitigate these costs by creating schedules that are less likely to get disrupted or schedules that are easier to repair when there are disruptions. In this paper, we present a robust optimization model for the crew pairing problem, which generates crew schedules that are less likely to get disrupted. Our model allows adding robustness without requiring detailed knowledge of the underlying delay distributions. Moreover, our model allows us to capture in detail the delay propagation through crew connections and the complex cost structure of the payand-credit crew salary scheme, thus enabling us to find a good trade-off between the deterministic component of the planned costs on the one hand and the expected delay and disruption costs on the other hand. Our robust crew pairing model is based on a deterministic crew pairing model formulated as a mixed-integer linear program. The robust version that we propose retains the linearity of the constraints and objective function and thus can be handled by commercial solvers, which facilitates its implementation in practice. We propose and implement a new solution algorithm for solving our model to optimality. Several optimal solutions with varying robustness levels are compared for the network of a moderate-size airline in the United States. We test the model's solutions in a simulation environment using real-world delay data. Our simulation results show that the robust crew pairing solutions lead to lower delays and fewer instances of operational infeasibilities, thus requiring fewer recovery actions to address them. We find that, with the inclusion of robustness, it is possible to generate crew pairing solutions that significantly reduce the delay and disruption costs with only a small increase in planned costs.