Scheduling Aircraft Landings—The Static Case

Abstract

In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a planeInthispaper,weconsidertheproblemofscheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time on a runway for each plane in a given set of planes such that each plane lands within a predetermined time window, and that separation criteria between the landing of a plane, and the landing of all successive planes, are respected.This paper is organized as follows. In Section 1, we set the problem in context. In Section 2, we present a mixed-integer zero-one formulation of the problem for the single runway case. We then discuss previous work on the problem in Section 3. In Section 4, we extend the formulation to the multiple runway case, and, in Section 5, we strengthen the linear programming (LP) relaxations of these formulations by introducing additional constraints. These formulations can be solved using LP-based tree search. An effective heuristic for the problem (for any number of runways) is presented in Section 6. Computational results for both the heuristic and the optimal algorithm for a number of test problems involving up to 50 planes and four runways are presented in Section 7.It is important to note here that, although throughout this paper we shall typically refer to planes landing, the models presented in this paper are applicable to problems involving just takeoffs only and to problems involving a mix of landings and takeoffs on the same runway. We should also stress here that we are dealing only with the static case. In other words, we are dealing with the off-line case where we have complete knowledge of the set of planes that are going to land. The dynamic, or on-line, case, where decisions about the landing times for planes must be made as time passes and the situation changes (planes land, new planes appear, etc.) is the subject of a separate paper (BEASLEY et al., 1995).

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

“…For example, many papers discuss the Aircraft Landing Problem (ALP), e.g., Beasley et al (2000) and Lieder et al (2015). The predominant objective is to minimize the total earliness/tardiness penalties, but the resources (runways) are assumed to be identical.…”

“…The following model is based on Beasley et al (2000) but considers hierarchical QLs. The sets, parameters, and decision variables are summarized in Table 2.…”

A Metaheuristic Approach to Aircraft Departure Scheduling at London Heathrow Airport

“…Previous research has looked at the arrivals problem with the goal being to order arriving aircraft for a single runway so as to either minimise the total completion time or to minimise the total deviation from an ideal arrival time for each aircraft. Mixed integer zero-one formulations were presented in [6] and Genetic Algorithms were shown to be effective in [7].…”

Routing of Airplanes to Two Runways: Monotonicity of Optimal Controls

“…in [3] where also a survey over different approaches is given. Deterministic models as in [3] often assume that a set of airplanes to be scheduled and routed is given.…”

“…in [3] where also a survey over different approaches is given. Deterministic models as in [3] often assume that a set of airplanes to be scheduled and routed is given. This allows to take into account more than one arrival and optimal schedules for a single set of aircrafts are obtained by mixed linear optimisation.…”