An aircraft scheduling problem posed by Armstrong and Cook is shown to be equivalent to an n-task, m-parallel machine problem, with start-times and deadlines. A forwards enumeration-type algorithm is presented, which generates feasible schedules for all problems in certain general classes, if they exist. Exclusion rules are discussed which improve the computational efficiency of the method. Extensions to more general problems, including precedence relationships among the tasks, and non-identical machines, are also described.