This study investigates the effects of the trade-off between fuel consumption and flight time on optimal merging trajectories with allocation optimization. A merging optimization method that simultaneously optimizes arrival trajectories and the sequence of aircraft has the potential to improve future decision support systems for air traffic control. In addition, the merging optimization method is required to optimize allocation of the arrival aircraft to parallel runways because most

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... airports have parallel runways. The merging optimization method with allocation optimization has been developed in previous studies, but only fuel consumption was minimized. Furthermore, in practice, the total flight time must be minimized, and it is possible that the trade-off between minimizing fuel consumption and flight time affects the optimal solution of the merging trajectory. Numerical simulations are performed to demonstrate the variation of the optimal merging trajectory. In particular, this study focuses on the variation of allocation of aircraft, which is a discrete factor in the merging optimization problem. The simulation results show that the allocation of aircraft can change due to the trade-off between minimizing fuel consumption and flight time. The optimality of the allocation is confirmed by comparing with the simulation results with specified allocation.