Comment by bodhiandphysics

One thing to note is that airline crew scheduling is np-hard (trivially you can reduce Hamiltonian cycle to it). Ak interesting semi-empiricle fact about np-complete problems. Take a decision problem to determine if there is a schedule with k crews. Now there is some k’ that is the minimum such k. For many Np problem problems the difficulty of the decision problem is related to the ratio of k to k’. (Not all decision problems are like this… those that are are on the complexity class APX. As a quick rule of thumb however this works) In terms of airline scheduling this means that if you more crews than you strictly need, your algorithm is probably going to successfully schedule them. When the number of crews drops below some critical value… all hell breaks loose. Thinking about this in complexity terms is useful I think. He issue isn’t just bad software… with a small enough number of crews, all software is bad, unless P = NP