Earlier quoted context omitted.
I find it hard to believe that compute power is the limitation here… something like simulated annealing would probably provide a reasonable, even if far from optimal solution on a regular PC. I imagine the feeding all of the data and constraints in is a bigger issue, when there is a lot of confusion and disorganization.
It would, and that's likely what they're using - but it isn't perfect . When it becomes non-perfect and you get a number of events that throw it off (like storms causing certain legs from not getting completed to move the plane to the proper spot and holidays causing disproportionate load in certain parts of the network), then everything gets messy.
Maybe the airline industry needs AlphaScheduler deep learning with monte carlo tree search. Or stimulated annealing. These cheap short sighted stuffed suits with MBAs who think that a fat tail refers to some part of the airplane.