A Generalized Dynamic Programming Approach for a Departure Scheduling Problem

Abstract

Reducing the delays of the departing aircraft can potentially lead to improving the efficiency of the surface operations at airports. This paper addresses a departure scheduling problem with an objective to reduce total aircraft delays subject to timing and ordering constraints. The ordering constraints model the queuing area of airports where the aircraft align themselves in the form of chains before departing. By exploiting the structure of the problem, a generalized dynamic programming approach is presented to solve the departure scheduling problem optimally. Computational results indicate that the approach presented in this paper is reasonably fast, i.e., it takes less than one tenth of a second on average to solve a 40 aircraft problem. Also, the approach produces optimal sequences whose delay is approximately 12 minutes, on average, less than the delays produced by the First Come First Serve (FCFS) sequences.

Runway Scheduling Using Generalized Dynamic Programming

“…Rathinam et al extended the work done by Psaraftis for a runway scheduling problem by showing that it is necessary to keep track of the throughput while attempting to find a delay optimal aircraft runway schedules. While the authors in [10] present a fast solution for finding a set of pareto optimal aircraft runway schedules, they do not extend the formulation to incorporate necessary runway constraints where the triangle inequality is violated. For example, the authors in [10] only consider a problem where three departure queues are present and there exist no runway crossing operations, which are known to violate the triangle inequality.…”

“…The dynamic programming approach in [7] provides a useful state definition which was then used by Rathinam et al [10] in a generalized dynamic programming fashion to find a set of pareto optimal solutions with respect to both throughput and delay for departure aircraft only. Rathinam et al extended the work done by Psaraftis for a runway scheduling problem by showing that it is necessary to keep track of the throughput while attempting to find a delay optimal aircraft runway schedules.…”

“…The authors in [4] [6] show how all separation constraints can be incorporated and how departure queue assignments are possible. While mixed integer linear programs have the advantage of easily modeling a large class of optimization problems, their computation times are often unsuitable for real-time applications [8] [10]. Alternatively, researchers have devised methods for enabling faster computation of runway schedules through the use of dynamic programming techniques under Constrained Position Shifting (CPS) constraints.…”

“…While there are several attempts at finding efficient aircraft runway schedules in the literature, these attempts are either not well-suited for application because of large computation times [4][5] [6], do not provide aircraft runway schedules which are optimal for both throughput and delay [4][5] [6] [7][8] [9], or solve simpler variants of a runway scheduling problem [10][8] [7]. The authors in [4][5] [6], for instance, formulate a runway scheduling problem as a mixed integer linear program.…”

“…either delay or throughput) or explore heuristics that do not guarantee optimal aircraft runway schedules. Lastly, the authors in [7][8] [10] solve simpler variants of a runway scheduling problem by considering only departure aircraft, preventing large deviations from a first-comefirst-served solution, or ignoring realistic aircraft separation constraints which might violate the triangle inequality.…”