Quote Originally Posted by spongebue View Post
Oh, I'm sure the days of airline scheduling are still in full swing. Probably a lot more computer-aided, but I do know there is a lot that goes into airplane-route-timing planning. But I'm sure even those problems are so complex, no current computer can solve the problem in a reasonable amount of time. Geeks-in-training can check this wikipedia page: P versus NP - Simple English Wikipedia, the free encyclopedia

I don't know for sure that this is considered an "NP" problem, but with all the different factors to work with (aircraft availability, fares, expenses, expected passenger loads, etc) I would be absolutely shocked if it weren't.
To complicate all this factor in pilot and flight attendant scheduling and positioning aircraft for routine maintenance and having a ground crew to clean/resupply the aircraft for the next day.