Stochastic Optimization Models for Transferring Delay Along Flight Trajectories to Reduce Fuel Usage.

In a typical aviation environment today, the precise landing times of en route aircraft are not set until each aircraft approaches the airspace adjacent to the destination airport. In times of congestion, it is not unusual for air traffic controllers to subject arriving aircraft to various maneuvers so as to create an orderly flow of aircraft onto an arrival runway. Typical maneuvers might include flying in zigzag patterns and flying in circular holding patterns, as well as others. These maneuvers serve to delay the arrival time of the flight. On the other hand, if the arrival time was established much earlier, then that delay could be realized by having the aircraft fly slower while still at a higher altitude, which would burn much less fuel than the described maneuvers. Three integer programming models are proposed to assign delay to aircraft approaching a single airport, well in advance of each aircraft's entry into the terminal airspace. The baseline model is deterministic and seeks to maximize the available throughput at the runway over a rolling horizon. The latter two models are stochastic and account for uncertainty regarding the status and controllability of certain flights. The first stochastic model is scenario based, while the second relies on a functional approximation of uncertainty. The results of computational experiments show that these approaches can transfer a considerable portion of the delay that would otherwise occur in the terminal area to the en route phase of flight, and also that the stochastic models are noticeably more effective. The model relying on functional approximation shows particular promise because of its efficient run time. The delay transfer yielded by each model resulted in significant predicted fuel savings. The functional approximation model performed particularly well under declining operational conditions, demonstrating itself to be a promising means of achieving delay transfer. [ABSTRACT FROM AUTHOR]