Arrival Manager (AMAN) 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 (IAF) 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 90%. Moreover, assuming that air traffic controllers (ATCs) schedule landings in a first-come first-served order, the ATC expected workload in the terminal area can be decreased by more than 98%, while the expected landing rate remains unchanged. 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.