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Schedule Design Optimization 199
to it, and because the number of possible flight schedules is, practically speaking,
unlimited. A sequential approach, in which schedules are repeatedly generated and
the fleet assignment problem is then solved for each schedule, is both impractical and
non-optimal in the sense that it cannot guarantee that optimal flight schedules will be
found.
The observation above, that flight schedule changes accompanied by new fleeting deci-
sions can result in more productive use of the airline’s fleet, is true even when the airline’s
bank structure at its hubs is maintained. An incremental schedule optimization model was
solved for a large US airline to determine revised flight schedules and fleet assignments,
allowing small shifts from the current schedule in the departure times of flights, while
maintaining the airline’s connecting banks at its hubs. The result was a reduction of
0.55% (two aircraft) in the number of aircraft needed to operate the flight schedule, and
additional expected annual operating cost savings and increased revenue capture of $50
million (Rexing et al., 2000).
Increased aircraft productivity results in less aircraft idle time, allowing the same set
of flight legs to be operated with fewer aircraft, or, conversely, providing the airline with
the opportunity to operate more flight legs. An incremental schedule optimization model,
therefore, should allow for the inclusion of additional flight legs, and, hence, should
also allow for the removal of existing flight legs. Associated with retiming, adding and
eliminating flight legs in the network, however, is an important dynamic: that of shifting
passenger demands. It is well documented that: (1) unconstrained market demand for a
carrier is a function of its flight schedule (with frequency of service being one critical
element); and (2) total market demand can change as a result of changes in the flight
schedule (Simpson and Belobaba, 1992). As an illustration of this, consider the removal of
a flight leg from a connecting bank. Its removal can impact passengers from many markets
because in addition to carrying local passengers from the leg’s origin to its destination,
the removed leg carries a significant number of connecting passengers from other markets
making use of that leg. From the viewpoint of the passengers in those markets, the quality
of service is deteriorated because the frequency of (connecting) service is decreased. The