The growing global air traffic has necessitated more efficient ground management in airports, especially during peak hours. Current approaches mainly consist of radar-based systems and radio communications, which provide limited visual assistance. Hence, Decision Support Systems (DSS) are designed to assist human Air Traffic Controllers (ATCos) by providing reliable recommendations based on current data and situations. The Airport Ground Optimizer (AGO) is a DSS designed for ATCos to manage the complexities of ground traffic in airports. It is based on advanced optimization algorithms and intuitive user interfaces, offering an enhanced operational experience. AGO uses mixed-integer programming (AGO-MIP) and stochastic programming (AGO-STC) to detect conflicts based on expected gate release and taxi times, and then optimizes the entire schedule to minimize hold fuels, resolve conflicts, and reduce fuel consumption, emissions, and delay times. Its key strength lies in translating complex mathematical solutions into user-friendly visual representations. AGO's core functionality includes comprehensive visualizations such as position charts, delay graphs, and potential conflict maps, providing a clear, real-time picture of ground operations for informed decision-making. AGO's queue and gate occupancy analysis calculates and visualizes the maximum queue length and concurrent number of aircraft at gates, enhancing airport capacity, reducing aircraft waiting times, and streamlining ground traffic flow. Simulated in a high-traffic Turkish airport layout, AGO-MIP demonstrated significant improvement in operational efficiency compared to traditional First Come First Served (FCFS) approach. AGO outperformed the traditional FCFS approach, reducing hold fuel by 27.9%, cutting delay time by 21.6%, lowering HC, CO, and NOx emissions by 16.4%, 22.5%, and 29.3% respectively, and decreasing the maximum queue length and its duration by 15.3% and 26.6%, as well as decreasing the number of delayed aircraft by 4.8%. The AGO-STC is also tested using pushback release uncertainties in the case airport, providing robust and feasible sequences, clear feedback for all possible scenarios, and detailed outcomes for each scenario. The study concludes by discussing potential developments and current issues of the tool in detail.