The overall structure of our MATLAB simulation is that of a nonlinear binary integer program. More specifically, the program is a scheduling problem where the objective is to minimize total delay time. The program seeks to make flight scheduling decisions to optimize this objective. For our program, we chose to refine our analysis to only one gate at Lambert Airport, A10, on a single day, October 1st, 2013 (as stated earlier). We did not have the time to attempt to optimize an entire airport or terminal schedule; therefore, we focused on one gate in a given day to limit the complexity of the problem. The general structure of the program can be seen in the figure below. The model’s input is a vector of scheduling decisions. The vector has a length of 60, with each value representing a 15-minute interval time slot from 6:00 am to 9:00 pm. We made the assumption of 15 minutes between each potential flight in order to account for the boarding process at the gate. If a flight is scheduled at a given time, the corresponding position has a value of 1. If there is no flight scheduled for that time, then the corresponding time slot has a value of 0. For example, there are flights scheduled at 6:00 am and 6:30 am, but the gate is vacant at 6:15 am and 6:45 am. In this input scenario, the first four entries in our scheduling vector would be [1 0 1 0 …].
Our program then takes this input vector of scheduled times and runs a Monte Carlo simulation in what we call Min Function. The simulation runs through 1,000 random scenarios that will result in different total delays at the gate for the day (more detail on the structure of this simulation will follow). An average of these 1,000 scenarios is then outputted as Total Delay. With the structure of our binary integer program completed, we attempted to use MATLAB’s nonlinear optimization function, fmincon, to make the scheduling decisions that should minimize the output, Total Delay.
Our program then takes this input vector of scheduled times and runs a Monte Carlo simulation in what we call Min Function. The simulation runs through 1,000 random scenarios that will result in different total delays at the gate for the day (more detail on the structure of this simulation will follow). An average of these 1,000 scenarios is then outputted as Total Delay. With the structure of our binary integer program completed, we attempted to use MATLAB’s nonlinear optimization function, fmincon, to make the scheduling decisions that should minimize the output, Total Delay.