Modified Mixed Integer Linear Program for Airport Departure Scheduling

A modified mixed integer linear program is presented for scheduling departure and arrival aircraft at airport runways in the form of deterministic optimization problem. The previous formulation explicitly considers practical constraints introduced at the airport such as wake vortex separation requirement and miles-in-trail separation as well as an optional prioritization scheme using time windows; however, several problems are observed from using this method in practical use. First, a new term is introduced in the formulation in order to capture the actual delay of each flight by storing information from each iteration during simulation. Furthermore, a weight factor by saturation term is introduced in the objective function in order to impose heavier cost on certain aircraft with longer delay time. Weight factor by saturation term in every iteration during simulation only depends on the results from one previous iteration since the linearity of the objective function is desired to be kept for simplicity and low computational cost. Three different functions for the weight factor by saturation are presented along with the sensitivity analysis in order to find the most appropriate parameters for each method. Results from all three methods indicate the improvement from the previous formulation since the maximum total delay of departure is significantly reduced using the modified MILP formulation with the weight factor by saturation. This simple revision can be applied to other scheduling problems with more practical constraints and parameters for specified airport type and configuration.