Runway sequencing with holding patterns

We study a scheduling problem, motivated by air-traffic control, in which a set of aircrafts are about to land on a single runway. When coming close to the landing area of the airport, a set of time windows in which the landing is possible, is automatically assigned to each aircraft. The objective is to maximize the minimum time elapsed between any two consecutive landings. We study the complexity of the problem and describe several special cases that can be solved in polynomial time. We also provide a compact Mixed Integer Programming formulation that allows us to solve large instances of the general poblem when all time windows have the same size. Finally, we introduce a general hybrid branch and cut framework, based on Constraint Programming and Mixed Integer Programming, to solve the problem with arbitrary time windows. Experimental results are reported.