Enhanced Models for a Mixed Arrival-Departure Aircraft Sequencing Problem
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.