A Closed-Form Solution to Multi-Point Scheduling Problems

A closed-form algorithm is proposed as a tool by which aircraft can be scheduled through an arbitrary number of scheduling points within allowable time constraints. The algorithm supports the specification of one or more time constraints at each point, along with minimum and maximum allowable travel-time constraints between points. A constraint algebra that simplifies the expression of time constraint calculations is used to formulate the algorithm. An example is then presented of an automated scheduler that uses constraint algebra and the new algorithm. The scheduler implements prospective operations for San Francisco International airport that is able to accommodate formation landings of aircraft pairs on closely spaced parallel runways for specified speed and timing constraints. A simulation of the scheduler shows that allowing flights to land in formation on two closely spaced parallel runways can reduce flight delays by 72% to 98% by enabling use of a second runway under adverse weather conditions when compared with the current single runway operation.