In airline crew rostering, pilots’ requests to operate specific flights need to be evaluated efficiently to avoid inefficient schedules. Despite the relevance of correctly assessing and granting crew requests, this topic has received very little attention in the literature. In this paper, we address the case this process is a dynamic problem, in which flight requests are submitted while others have already been granted and pre-assigned. This is the first work to dynamically model flight requests during the crew rostering process. We propose a simulation-trained neural-network algorithm to evaluate flight requests, providing a systematic way of assessing flight requests and supporting the definition of a cost-efficient request granting policy. To train and test this algorithm, we developed an innovative rolling rostering framework that captures the dynamic process in practice. The framework relies on an integer linear programming crew rostering model solved with the help of a column-generation algorithm. The neural-network algorithm is trained and tested in a case study with a major European airline. The results show that the algorithm is more effective than the current practice at the airline, granting 22% more requests while using the same workforce to operate the flight schedule.