The Ground Delay Program (GDP) relies heavily on the capacity of the subject airport, which, due to its uncertainty, adds to the difficulty and suboptimality of GDP operation. This paper proposes a framework for the joint optimization of GDP key parameters including file time, end time, and distance. These parameters are articulated and incorporated in a GDP model, based on which an optimization problem is proposed and solved under uncertain airport capacity. Unlike existing literature, this paper explicitly calculates the optimal GDP file time, which could significantly reduce the delay times as shown in our numerical study. We also propose a joint GDP end-time-and-distance model solved with genetic algorithm. The optimization problem takes into account the GDP operational efficiency, airline and flight equity, and Air Traffic Control (ATC) risks. A simulation study with real-world data is undertaken to demonstrate the advantage of the proposed framework. It is shown that, in comparison with the current GDP in operation, the proposed solution reduces the total delay time, unnecessary ground delay, and unnecessary ground delay flights by 14.7%, 50.8%, and 48.3%, respectively. The proposed GDP strategy has the potential to effectively reduce the overall delay while maintaining the ATC safety risk within an acceptable level.