We develop certain extensions of optimization based conflict resolution methods in air traffic control. The problem considered concerns the scheduling of the crossing times of a set of aircraft through a metering fix, while maintaining aircraft separation. First, we show how to solve this combined path planning and scheduling problem using mixed integer geometric programming. Second, the objective function used to determine the aircraft ordering at the fix is not given a priori but needs to be obtained from the airlines, which are strategic profit maximizing agents and could lie about their true cost. In order to realign individual and global objectives, we study the use of the Clarke-Groves mechanism in this context, which aims at extracting the true utility functions from the airlines using side-payments to the FAA.