amenable to optimization. With so many possible
decisions, it is difficult to find feasible—let alone
optimal—solutions manually. Moreover, crews represent
the airlines’ second highest operating cost after
fuel, so even slight improvements in their utilization
can translate into significant savings.
For these reasons, airline crew scheduling has garnered
considerable attention, with research spanning
decades. Arabeyre et al. (1969) published a survey
of early research activities on the topic. At that
time, because of large problem size and lack of
advanced techniques and sufficient computing capabilities,
heuristics were employed to find improved
crew solutions.
Since then, researchers have continued to work on
the crew scheduling problem, seeking more efficient
solution approaches, expanding models to capture
more of the intricacies of the crew scheduling problem,
and integrating the crew problem with other
airline scheduling problems. Recent detailed descriptions
of the airline crew scheduling problem are
included in the survey papers by Desaulniers et al.
(1998), Clarke and Smith (2000) and Barnhart et al.
(2003).
Even today, the crew scheduling problem is typically
broken into two sequentially solved subproblems,
the crew pairing problem and the crew assignment
problem:
(1) The crew pairing problem. The problem generates
minimum-cost, multiple-day work schedules, called
pairings. Regulatory agencies and collective bargaining
agreements specify the many work rules that
define how flight legs can be combined to create feasible
schedules. Work-rule restrictions include limits
on the maximum number of hours worked in a day,
the minimum number of hours of rest between work
periods, and the maximum time the crew may be
away from their home base. Even with these limitations,
the number of feasible pairings measures in
the billions for major U.S. airlines. The cost structure
of pairings adds further complexity, with cost typically
represented as a nonlinear function of flying
time, total elapsed work time, and total time away
from base.
(2) The crew assignment problem. This problem combines
these pairings into equitable and efficient