Aircraft landing problems with aircraft classes

Abstract

This paper focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft's landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount of earliness and lateness, respectively. The objective is to minimize overall cost. We consider the set of aircraft being partitioned into aircraft classes such that two aircraft of the same class are equal with respect to wake turbulence. We develop algorithms to solve the corresponding problem. Analyzing the worst case run time behavior, we show that our algorithms run in polynomial time for fairly general cases of the problem.Moreover, we present integer programming models. We show by means of a computational study how optimality properties can be used to increase efficiency of standard solvers.

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

“…In this paper, however, we assume that both separation requirements and delay cost functions are operation class-dependent. Briskorn and Stolletz (2014) prove that, under these assumptions, the ASP is polynomial in the number of runway operations but exponential in the number of runways and operation classes by defining an exact DP with a polynomial state space. Bennell et al (2013) provide an extensive literature overview on airport runway operations, featuring articles up to 2009.…”

“…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.…”

Task scheduling in long-term care facilities: A client-centered approach

“…It can be shown that, for problem instances that have a feasible solution, there is always an optimal solution in which all tasks of the same type are assigned in FCFS discipline (Briskorn and Stolletz, 2014). Hence, we can define a set of all pairs of tasks with a pre-determined order of start times, either because they have the same duration and QL or because their order is implied by their time windows:…”

Mechanisms for scheduling games with selfish players

“…It models economic situations where clients queue for a single scarce resource, e.g. scheduling aircraft landing, where multiple planes have to be scheduled to land on one runway [5,7]. At the same time, the problem is the private information version of one of the most basic and classical machine scheduling models, namely to minimize the total weighted completion time of a given number of non-preemptive jobs with weights w j and processing times p j on a single machine.…”