Enhanced Models for a Mixed Arrival-Departure Aircraft Sequencing Problem

Abstract

This paper addresses the static aircraft sequencing problem over a mixed-mode single runway (or closely interacting parallel runways), which commonly constitutes a critical bottleneck at airports. In contrast with disjunctive formulations, our modeling approach takes advantage of the underlying structure of an asymmetric traveling salesman problem with time-windows. This enables the development of efficient preprocessing and probing procedures, and motivates the derivation of several classes of valid inequalities along with partial convex hull representations to enhance problem solvability via tighter reformulations. The lifted model is further embedded within the framework of two proposed heuristics that are compared against the traditional first-come first-served (FCFS) heuristic with landing priority: an optimized FCFS policy (OFCFS) and a threshold-based suboptimized heuristic (TSH) with an a priori fixing of the relative order of aircraft that are sufficiently time-separated. Computational results using real data based on Doha International Airport (DOH) as well as simulated instances are reported to demonstrate the efficacy of the proposed exact and heuristic solution methods. In particular, for the DOH instances, heuristics OFCFS and TSH achieved an attractive runway utilization (4.3% and 5.0% makespan reduction, respectively, over the base FCFS policy with landing priority), while exhibiting limited aircraft position deviations (0.45 and 0.49 deviations on average, respectively, from the base FCFS positions with landing priority, with similar results being obtained for the simulated instances). The superiority of the proposed optimization models over previous disjunctive formulations is also demonstrated for challenging problem instances, resulting in over 50% CPU savings for the larger instances in our test-bed.

A Review for Aircraft Landing Problem

“…Some studies take departing flights into account without considering the trigonometric inequality of interval. Ghoniem A [13] solved this problem by introducing new simple interval constraints in two aircrafts of identical weight level and operation to ensure the inequality. However, the above method can get better results for arrivals, and departures do not get a good arrangement.…”

An evolutionary approach for dynamic single-runway arrival sequencing and scheduling problem

“…However, the ASS problems of shortening the required landing time (Balakrishnan and Chandran 2006;Bojanowski et al 2011;Ghoniem et al 2014;Hrikiopoulo and Neogi 2011;Hu and Chen 2005a, b;Malaek and Naderi 2008) and minimizing the total airborne delay (Hu and Chen 2005a, b;Hu and Di 2008;Sun and Hua 2009;Wang et al 2008;Zhan et al 2010) are essentially different optimization problems (Psaraftis 1978). A sequence that has a lower airborne delay may lead to a longer required landing time.…”

Scheduling Aircraft Take-Offs and Landings on Interdependent and Heterogeneous Runways

“…Ghoniem et al (2014) present a rule-based approach (''optimized FCFS") and a MIP-based approach (''threshold-based suboptimized heuristic"). They evaluate their solution quality using practice data from Doha International Airport.…”

“…The most cited MIP formulation by Beasley et al (2000) considers complete separation and interdependent runways. Recently, several authors proposed reformulations or valid inequalities (VI) to tighten this formulation (Briskorn and Stolletz, 2014;Farhadi et al, 2014;Ghoniem et al, 2014;. They generally outperform the MIP by Beasley et al (2000) but still exhibit prohibitive computation times for all except small problem instances, and they do not consider interdependent runways.…”

“…We also assume ordered time windows, that is, we assume that the latest possible operation times of all pairs ða; a 0 Þ of aircraft are in the same order as their target times, i.e., T a 6 T a 0 () L a 6 L a 0 . Under these assumptions, all feasible ASP instances have an optimal solution, in which the aircraft of the same aircraft class are scheduled FCFS, i.e., for wðaÞ ¼ wða 0 Þ^T a < T a 0 ; C a 6 C a 0 holds for all ða; a 0 2 A; a -a 0 Þ (Briskorn and Stolletz, 2014;Ghoniem et al, 2014). There are no sequencing restrictions for pairs of operations from different classes.…”