Stochastic
Optimization Models for Transferring Delay Along Flight Trajectories to Reduce
Fuel Usage
James C.
Jones, David J. Lovell, and Michael O. Ball
Transportation
Science,
vol. 52(1), pp. 134-149
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.