Accommodating new flights into an existing airline flight schedule

We present two novel approaches to alter a flight network for introducing new flights while maximizing airline's profit. A key feature of the first approach is to adjust the aircraft cruise speed to compensate for the block times of the new flights, trading off flying time and fuel burn. In the second approach, we introduce aircraft swapping as an additional mechanism to provide greater flexibility in reducing the incremental fuel cost and adjusting the capacity. The nonlinear fuel-burn function and the binary aircraft swap and assignment decisions complicate the optimization problem significantly. We propose strong mixed-integer conic quadratic formulations to overcome the computational difficulties. The reformulations enable solving instances with 300 flights from a major U.S. airline optimally within reasonable compute times.