Airline delay propagation: Estimation and modeling in daily operations

Airline companies try to increase their revenues, service level, and customer satisfaction in a highly competitive global sector. Airline schedule planning is crucial for airline companies to reach these objectives. Airline schedules are usually constructed assuming that there will be no disruption. But in reality, there are plenty of incidences such as weather conditions, mechanical failure, air traffic, and security issues that cause delays and disrupt daily operations. Even though it is impossible to avoid the delay completely, there are ways to decrease the propagation of the delay. To cope with delay propagation, airlines insert idle time, known as slack, between flights in the schedule. However, idle time means inefficient use of aircraft resources. Thus, adjusting the idle time in the schedule dynamically during daily operations is a critical task for planning departments. In this study, flight time rescheduling and aircraft swapping are used to decrease the expected delay propagation. By using these two options, the scheduled slack is clustered at flights that are prone to delay propagation. We aim to reduce the negative consequences of delay proactively while keeping the total slack constant in the schedule. Keeping the slack constant helps reduce other adverse network effects and enables the rest of the plan to be still intact for the future. We propose to use multivariate kernel density estimation to estimate the probability of independent delay from flight data and argue that this is a practical and effective way of estimating such distributions for daily airline operations. We use that estimation in two mathematical programming formulations: the single layer model, and the single layer model with aircraft swapping option to minimize the expected propagated delay. Since the latter model is a non-linear model, we also introduce an approximation for it to overcome the computational issues in solving large instances of the problem. After illustrating our approach on a small set of data, we report our computational results using flight schedule data from Turkish Airlines augmented with weather related information. We argue that the proposed models help decrease the expected delay propagation by up to 90% allowing a 15-min change in the schedule and swapping aircraft when necessary.