A basic start would be looking at network flow problems. While they don't extend to the complexity of real world airline scheduling, you can construct a simplif

A basic start would be looking at network flow problems. While they don't extend to the complexity of real world airline scheduling, you can construct a simplified airline scheduling problem with it. Additionally, one of the methods to solve these problems, linear programming, does extend to integer linear programming which can be used to solve the more complicated cases (in non-deterministic polynomial time).