I’ve worked on airline scheduling system and solving to optionally is indeed NP-hard and scales badly. However you can get to a very good spot with heuristics.

I’ve worked on airline scheduling system and solving to optionally is indeed NP-hard and scales badly. However you can get to a very good spot with heuristics. This particular issue with SW looks like bad data collection(crew has to phone their location!) and a combination of lack of reserves, bad weather and holidays surge.