Unfortunately, MATLAB’s nonlinear optimizer, fmincon, could not find an optimal solution to our objective, Min Function. MATLAB stopped searching for an optimal solution due to processing time and outputted that no feasible solution was found. Upon further examination of our code, we found that MATLAB failed because of our nonlinear equality constraint. MATLAB does not have a solver for nonlinear binary integer programs. Therefore, we manipulated the constraints within fmincon to create such a program. Fmincon was unable to handle this manipulation. Looking forward, we would attempt to find different software that could handle an integer program in a nonlinear framework.
Had the code worked, we illustrate what an optimal solution might look like in the figure below:
The 1’s in the “Scheduling Decision” column correspond to when the 25 flights at gate A10 would be scheduled. The 0’s are the time slots when the gate would be vacant. If this scheduling decision is inputted into Min Function, the total delay would come out to be 130.0362 minutes.
Had the code worked, we illustrate what an optimal solution might look like in the figure below:
The 1’s in the “Scheduling Decision” column correspond to when the 25 flights at gate A10 would be scheduled. The 0’s are the time slots when the gate would be vacant. If this scheduling decision is inputted into Min Function, the total delay would come out to be 130.0362 minutes.