In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneously taking into account three important issues: (i) the model explicitly incorporates uncertainty in the airport capacities; (ii) it also considers the trade-off between airport arrivals and departures, which is a crucial issue in any hub airport; and (iii) it takes into account the interactions between different hubs. The level of aggregation proposed for the mathematical model allows us to solve realistic size instances with a commercial solver on a PC. Moreover it allows us to compute solutions which are perfectly consistent with the Collaborative Decision-Making (CDM) procedure in ATFM, widely adopted in the USA and which is currently receiving a lot of attention in Europe. In fact, the proposed model suggests the number of flights that should be delayed, a decision that belongs to the ATFM Authority, rather than assigning delays to individual aircraft.