The applied math discipline behind it is called Operations Research (OR). The field was made popular by the US army planners back in WW2. Now it is used by nearly everyone from the airlines, to the big banks, and even Waffle House (they are actually one of the best in the OR business). The discipline is mostly about modeling decisions problems that require minimization of certain quantities such as time, delays, costs, etc as standard classes of mathematical optimization problems. Preferably linear or convex optimization problems since they are tractable up to large sizes. The main difficulties lies in making useful models and sometimes solving an intractable optimization problem. The models are also usually stochastic since most of the time the available data only gives you probabilities not certainties.

One of the biggest buzzword in current research in airlines OR is:

Collaborative Decision Making (CDM) - essentially all the airlines in an airport combining their operations to minimize overall delays and congestion in the airport. The eurocontrol's website on CDM is http://www.euro-cdm.org/ The FAA's is http://cdm.fly.faa.gov/