point-to-point networks, researchers have integrated
fleet assignment and aircraft routing models, as in
Desaulniers et al. (1997) and Barnhart et al. (1998a).
This has the effect of substantially expanding the aircraft
routing model to include multiple fleet types,
instead of a single aircraft type. The number of constraints
for large airlines is often less than a few thousand,
but there are many billions of possible variables.
For hub-and-spoke networks, however, the increased
size and complexity of this integrated model is rarely
warranted. Instead, feasible solutions are typically
generated using a slightly modified sequential solution
approach in which an altered fleeting model is
first solved and then the routing model is solved.
The modified fleet assignment model contains pseudomaintenance
constraints to ensure that sufficient numbers
of aircraft of each type are located at maintenance
stations periodically. In hub-and-spoke networks
with banks containing many aircraft together on the
ground at the same time, these maintenance constraints
are often sufficient to ensure that the resulting
fleet assignment has associated feasible maintenance
routings.
In addition to the possibility of generating infeasible
solutions, a disadvantage of the sequential
solution approach to aircraft and crew planning is
that aircraft routing solutions limit possible crew
scheduling opportunities, potentially causing crew
costs to increase significantly. The linkage between
aircraft routing and crew scheduling occurs because
a crewmember can connect between two flight legs
separated by less than the minimum required connection
time only if the same aircraft is assigned to both
legs. To account for this, Klabjan et al. (2002) swap
the order of the problems and solve the crew pairing
problem before the maintenance routing problem.
This approach has the advantage of generating optimal
crew solutions, but it does not ensure that for
the optimized crew solution there is a corresponding
maintenance-feasible solution. To achieve crew
optimality and maintenance feasibility, Cordeau et al.
(2000) and Cohn and Barnhart (2003) integrate the
basic maintenance routing and crew pairing models.
2.4. Crew Scheduling
Crew scheduling problems with numerous, complex
rules, and well-defined costs are particularly