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In this paper, we consider the airport-landing problem of scheduling different types of aircraft on a single runway. Since the minimum allowable landing separation time between two consecutive aircraft depends on the relative weight of both aircraft, this is a state-dependent scheduling problem, which, in the general case, is NP-hard. We attempt to modify the aircraft landing sequence from the traditionally used “first-come-first-served” (FCFS) order to be able to land more aircraft in a given period of time. Given a set of planes, the goal is to find a sequence such that no plane can land before it is actually available for landing, the minimum safety separation between two consecutive planes is always satisfied, and the total landing time (makespan) is minimized. Based on the Federal Aviation Administration (FAA) partition of aircraft into weight categories, our algorithm provides a polynomial-time feasibility condition for scheduling a set of planes in a given time interval. It ensures that the Aircraft Scheduling Problem (ASP) presented earlier is not NP-complete and allows us to develop possible practical real-time air traffic control (ATC) execution policies.