Optimising the flight turnaround schedules : an improved sliding time windows approach based on MILP and CP models

This paper addresses the scheduling of turnaround operations for flights in civil airports. A series of complex issues, including the heterogeneity of flights and operators, resource constraints on turnaround operations, temporal restrictions and alternative service patterns of turnaround operations, multi-functional operators, multi-trip services and multi-to-one services, are jointedly considered. We propose two formulations for the problem: A mixed-integer linear programming (MILP) model, and a constraint programming (CP) model. For comparison purpose, we also present simplified versions of the models in which the multi-to-one services are prohibited. The uncertainty are incorporated by modifying the models based on robust optimisation principles. The numerical experiments are conducted using instances generated based on real flight data at Beijing Capital International Airport. It is shown that under current computer configurations, small-scale instances can be solved to the optimum by CPLEX within an acceptable period of time using the MILP model, while moderate-scale instances can be tackled using the CP formulation. To cope with large-scale instances, an improved sliding time window method is developed, and evaluated with different parameter combinations, showing that practical turnaround schedule would best be updated two to three times per hour. Besides, after a case study in both static and stochastic scenarios, we illustrate that multi-to-one services should be specifically considered and highlighted, for their existence could significantly improve the operator utilisation rate and reduce flight delay, especially when the uncertainties are taken into account.