In terminal airspace, integrating arrivals, departures, and surface operations with competing resources provides the potential of improving operational efficiency by removing barriers between different operations. This work develops a centralized stochastic scheduler for operations in a terminal area including airborne and surface operations using a non-dominated sorting genetic algorithm and Monte Carlo simulations. The scheduler handles competing resources between different flows, such as runway allocations, runway crossings, merges at departure fixes, and other interaction waypoints between arrivals and departures. The scheduler takes time-varied uncertainties into account in optimization as well. The scheduler is run sequentially to identify the best robust schedule for the next planning window. Resulting schedules determine routes, speeds or delays, and runway assignments subject to separation constraints at merging/diverging waypoints in the air and at runways (including runway crossings) on the surface. The Los Angeles terminal area was used as an example in experiments with a four-hour traffic scenario. The results showed that using stochastic schedulers can reduce flight time delay (airborne and ground) anywhere from 28% to 40% statistically compared to deterministic schedulers. Sensitivity studies on various planning horizons presented that trade-offs exist between planning horizons and achievable minimum delays. A twenty-minute planning horizon was found to be a bad choice because uncertainties increased with the look-ahead time. Eight minutes was promising for planning as it achieved the lowest delay compared to others. However, the results demonstrated that any duration from two minutes to eight minutes could be a good candidate as well. The results on runway usage showed that using the stochastic scheduler, runway makespans and occupancy were usually slightly lower than applying deterministic schedulers.