This dissertation conducts a systematic study of terminal area traffic management using optimization methods. The critical role that the airport plays in national airspace system is introduced. The challenges in managing complex terminal traffic are explained. The necessity and importance of the study is addressed. To assist human air traffic controllers in managing complex terminal traffic, our solution strategy is to calculate each flight's optimal arrival/departure schedule, to minimize the overall flight delay and runway congestion in the entire airport. Three solutions are developed in the thesis, including the static solution, the dynamic solution, and the stochastic solution. The static solution uses one computation and attempts to optimize the schedules of many flights arriving/departing the airport within a wide time window. The accuracy of its solution heavily relies on the quality of the predicted traffic situation acquired right before the computation. On the contrary, the dynamic solution attempts to divide the entire traffic flow into a series of small pieces, and optimize flight schedules piece by piece. It collects the latest traffic information before each computation and experiences far less computational load. Both static and dynamic solutions assume the traffic information to be explicitly known. They are inherently deterministic solutions. The third solution proposed in this thesis is a stochastic solution. It assumes that traffic information is not known with certain due to a variety of random factors in actual flight operations. This stochastic solution is mathematically and structurally designed to handle multiple sources of uncertainties in managing terminal traffic. In the last, the conclusion is given based upon the simulation tests of the three proposed runway scheduling solutions. Future work is also suggested.