The obvious goal of mathematical optimization is the first dimension - The best possible solution. In a crew pairing problem it means to find a set of crew pairings which covers all flights, satisfies all legality rules and operational constraints and minimises the cost for the airline. In a preferential bidding problem it means maximising the satisfaction of the crew, respecting the productivity requirements of the airline. Advancements in optimization technology, such as the solution of very large linear programs, branch and bound and decomposition methods have brought solution quality of crew pairing problems very close to optimality on fleets as large as 500 daily operations. In reality, however, the challenge to improve solution quality on very large problems is still there since the size of problems is constantly increasing. The most important drivers for increasing problem size are larger fleets and the integration of different business processes within airlines. Fleets for crew scheduling become larger because of common cockpit configurations and decisions to qualify cabin crew for multiple aircraft types. The integration of business processes suggest to solve crew pairing and crew assignment problems simultaneously. Integration of fleet assignment, crew pairing and schedule planning also offer an opportunity for further optimization, although the solution of these very large problems still remains a challenge.
The second dimension - The right problem, is too often omitted in scientific work for airlines. All systems of today solve a problem which is not exactly the real life problem, but an approximation, or a subproblem resembling the real life problem only to a certain extent. Even though the subproblem can be solved optimally, the underlying real life problem is only partially solved. To overcome this problem, designers of airline decision support systems have concentrated on advancing the modelling capabilities over the past few years. The development of rule modelling tools, such as the Carmen rule language used by all major European airlines, have enabled airlines to significantly increase the level of detail in optimization models. Airlines now include every hotel room, every positioning flight, every meal at actual cost in their optimization models. The tools are also used to model other quality criteria such as robustness, quality of service, and quality of life. All these refinements in modelling have practically eliminated the need for manual interaction in the solution process for crew pairing and crew assignment.
The third dimension is speed. In resource optimization, speed is an end in itself since it creates new opportunity for the user. If a crew scheduling problem can be solved in one day it can be useful in a production planning situation. However, if it is solved in one hour there is time for evaluating several scenarios and if it is solved in a minute the tool is powerful on the day of operation, and has a major impact on how the airline operates.
All three dimensions of optimizer performance are linked in the sense
that an improvement in one dimension will always be at the cost of compromise
in another dimension. The trade-off is largely an issue of configuration,
and airlines tend to prioritise the modelling dimension more than anything
else, since this is where the biggest potential for improvement currently
lies. Integration is the path for the future, and this poses tremendous
challenges for the operations research community and software companies
like Carmen Systems which lead the development of resource optimization
systems for the airline industry.