Optimal scheduling algorithm in point merge system including holding pattern based on mixed-integer linear programming

An optimal scheduling algorithm of the point merge system that considers a holding pattern is presented based on mixed-integer linear programming. The route structure of the point merge system is constructed by adopting virtual fixes, and appropriate constraints are included to integrate a holding pattern into the formulation of point merge system. The performance of the proposed point merge system holding algorithm is demonstrated by comparing with the point merge system and first-come first-served algorithms via Monte Carlo simulation. Simulation reveals that the point merge system holding algorithm shows the best performance in terms of delay reduction and intervention rate by air traffic controllers. The proposed point merge system holding algorithm is expected to assist human air traffic controllers as a decision support tool.