Air traffic flow becomes denser and more complex within terminal manoeuvering areas (TMAs) due to rapid growth rates in demand. Effective TMA arrival management plays a key role in the improvement of airspace capacity, flight efficiency and air traffic controller performance. This study proposes a mixed integer linear programming model for aircraft landing problems with area navigation (RNAV) route structure using three conflict resolution and sequencing techniques together: flexible route allocation, airspeed reduction and vector manoeuver. A two-step mixed integer linear programming model was developed that minimises total conflict resolution time and then total airborne delay using lexicographic goal programming. Experimental results demonstrate that the model can obtain conflict-free and time optimal aircraft trajectories for RNAV route structures.