Arrival Manager operational horizon, in Europe, is foreseen to be extended up to 500 nautical miles around destination airports. In this context, arrivals need to be sequenced and scheduled a few hours before landing, when uncertainty is still significant. A computational study, based on a two-stage stochastic program, is presented and discussed to address the arrival sequencing and scheduling problem under uncertainty. This preliminary study focuses on a single Initial Approach Fix and a single runway. Different problem characteristics, optimization parameters as well as fast solution methods for real-time implementation are analyzed in order to evaluate the viability of our approach. Paris Charles-De-Gaulle airport is taken as a case study. A simulation-based validation experiment shows that our approach can decrease the number of expected conflicts near the terminal area by up to 70%. Moreover, in a high-density traffic situation, the total time-to-lose inside the terminal area can be decreased by more than 71%, while the expected landing rate can be increased by 7.7%, compared to the first-come first-served policy. This computational study demonstrates that sequencing and scheduling arrivals under uncertainty, a few hours before landing, can successfully diminish the need for holding stacks by relying more on upstream linear holding.