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In this paper we present a solution methodology based on the stochastic branch and bound algorithm to find optimal, or close to optimal, solutions to the stochastic airport runway scheduling problem. The objective of the scheduling problem is to find a sequence of aircraft operations on one or several runways that minimizes the total makespan, given uncertain aircraft availability at the runway. Enhancements to the general stochastic branch and bound algorithm are proposed and we give the specific details pertaining to runway scheduling. We show how the algorithm can be terminated early with solutions that are close to optimal, and investigate the impact of the uncertainty level. The computational experiment indicates that the sequences obtained using the stochastic branch and bound algorithm have, on average, 5–7% shorter makespans than sequences obtained using deterministic sequencing models. In addition, the proposed algorithm is able to solve instances with 14 aircraft using less than 1 min of computation time.

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... Concernant les atterrissages, ces séparations sont d'abord indiquées en distance (NM) mais souvent converties en temps en utilisant des vitesses représentatives d'atterrissage [21,66] SH -6 6 7 7 8 UH -3 4 5 5 6 LH -4 3 5 5 6 UM -----5 LM - ...

... A notre connaissance, Sölveling, Solak, Clarke, et Johnson [65,66,67] sont les seuls auteursà avoir proposé des modèles de programmation stochastiqueà deuxétapes pour la version stochastique du problème d'ordonnancement des avions. Dans la suite, nous présentons ces contributions dans leur ordre de publication. ...

... Dans un article plus récent [66], Sölveling et Clarke ont réutilisé le branch-and-bound stochastique sur le problème d'ordonnancement des avions mais en redéfinissant les deux etapes de décision comme suit : ...

Dans le contexte d'une augmentation soutenue du trafic aérien et d'une faible marge d'expansion des capacités aéroportuaires, la pression s'accroît sur les aéroports les plus fréquentés pour une utilisation optimale de leur infrastructure, telle que les pistes, reconnues comme le goulot d'étranglement des opérations aériennes. De ce besoin opérationnel est né le problème d'ordonnancement des atterrissages d'avions, consistant à trouver pour les avions se présentant à un aéroport la séquence et les heures d'atterrissage optimales par rapport à certains critères (utilisation des pistes, coût total des retards, etc) tout en respectant des contraintes opérationnelles et de sécurité. En réponse à ce besoin également, depuis les années 1990 aux Etats-Unis et en Europe, des outils d'aide à la décision ont été mis à la disposition des contrôleurs aériens, afin de les assister dans leur tâche d'assurer la sécurité et surtout la performance des flux d'arrivée. Un certain nombre de travaux de recherche se sont focalisés sur le cas déterministe et statique du problème d'atterrissage d'avions. Cependant, le problème plus réaliste, de nature stochastique et dynamique, a reçu une attention moindre dans la littérature. De plus, dans le cadre du projet européen de modernisation des systèmes de gestion de trafic aérien, il a été proposé d'étendre l'horizon opérationnel des outils d'aide à la décision de manière à prendre en compte les avions plus loin de l'aéroport de destination. Cette extension de l'horizon opérationnel promet une meilleure gestion des flux d'arrivées via un ordonnancement précoce plus efficient. Néanmoins, elle est inévitablement accompagnée d'une détérioration de la qualité des données d'entrée, rendant indispensable la prise en compte de leur stochasticité.L'objectif de cette thèse est l'ordonnancement des arrivées d'avions, dans le cadre d'un horizon opérationnel étendu, où les heures effectives d'arrivée des avions sont incertaines. Plus précisèment, nous proposons une approche basée sur la programmation stochastique à deux étapes. En première étape, les avions sont pris en considération à 2 - 3 heures de leur atterrissage prévu à l'aéroport de destination. Il s'agit de les ordonnancer à un point de l'espace aérien aéroportuaire, appelé IAF (Initial Approach Fix). Les heures effectives de passage à ce point sont supposées suivre des distributions de probabilitéconnues. En pratique, cette incertitude peut engendrer un risque à la bonne séparation des avions nécessitant l'intervention des contrôleurs. Afin de limiter la charge de contrôle conséquente, nous introduisons des contraintes en probabilité traduisant le niveau de tolérance aux risques de sécurité à l'IAF après révélation de l'incertitude. La deuxième étape correspond au passage effectif des avions considérés à l'IAF. Comme l'incertitude est révélée, une décision de recours est prise afin d'ordonnancer les avions au seuil de piste en minimisant un critère de deuxième étape (charge de travail des contrôleurs, coût du retard, etc).La démonstration de faisabilité et une étude numérique de ce problème d'ordonnancement des arrivées d'avions en présence d'incertitude constituent la première contribution de la thèse. La modélisation de ce problème sous la forme d'un problème de programmatiion stochastique à deux étapes et sa résolution par décomposition de Benders constituentla deuxième contribution. Finalement, la troisième contribution étend le modèle proposé au cas opérationnel, plus réaliste où nous considérons plusieurs points d'approche initiale.

... The optimization of aircraft movement on the taxiway is a key problem [3]. This condition can further complicate other elements, such as runway ordering [4,5] and the distribution of stand/departure gates on the airport's surface [6]. Although taxiing on the airport surface is a small part of running an aircraft, it can significantly influence the operating costs and emissions of airports. ...

... Table 10 shows the environmental aircraft data. The fuel flows of Learjet35A, A320, and A333 under different taxiing states in ZULS, ZPPP, and ZSPD can be obtained by integrating the data in Table 9 into Equations (4), (5), and (6), respectively. Table 11 illustrates the results. ...

High-efficiency taxiing for safe operations is needed by all types of aircraft in busy airports to reduce congestion and lessen fuel consumption and carbon emissions. This task is a challenge in the operation and control of the airport’s surface. Previous studies on the optimization of aircraft taxiing on airport surfaces have rarely integrated waiting constraints on the taxiway into the multi-objective optimization of taxiing time and fuel emissions. Such studies also rarely combine changes to the airport’s environment (such as airport elevation, field pressure, temperature, etc.) with the multi-objective optimization of aircraft surface taxiing. In this study, a multi-objective optimization method for aircraft taxiing on an airport surface based on the airport’s environment and traffic conflicts is proposed. This study aims to achieve a Pareto optimized taxiing scheme in terms of taxiing time, fuel consumption, and pollutant emissions. This research has the following contents: (1) Previous calculations of aircraft taxiing pathways on the airport’s surface have been based on unimpeded aircraft taxiing. Waiting on the taxiway is excluded from the multi-objective optimization of taxiing time and fuel emissions. In this study, the waiting points were selected, and the speed curve was optimized. A multi-objective optimization scheme under aircraft taxiing obstacles was thus established. (2) On this basis, the fuel flow of different aircraft engines was modified with consideration to the aforementioned environmental airport differences, and a multi-objective optimization scheme for aircraft taxiing under different operating environments was also established. (3) A multi-objective optimization of the taxiing time and fuel consumption of different aircraft types was realized by acquiring their parameters and fuel consumption indexes. A case study based on the Shanghai Pudong International Airport was also performed in the present study. The taxiway from the 35R runway to the 551# stand in the Shanghai Pudong International Airport was optimized by the non-dominant sorting genetic algorithm II (NSGA-II). The taxiing time, fuel consumption, and pollutant emissions at this airport were compared with those of the Kunming Changshui International Airport and Lhasa Gonggar International Airport, which have different airport environments. Our research conclusions will provide the operations and control departments of airports a reference to determine optimal taxiing schemes.

... As a consequence, several renovation projects have been launched, such as the Single European Sky ATM Research (SESAR) in Europe, the Next Generation Air Transportation System (NextGen) in the United States, and the Aviation System Block Upgrades (ASBU) framework from International Civil Aviation Organization (ICAO), to enhance the levels of safety, capacity, efficiency and environmental sustainability. In the ATM domain, conflict detection and resolution [2], aircraft sequencing and scheduling [3], trajectory based operation [4] are the most promising novel concepts and advanced technologies of the above renovation projects. And these concepts and technologies could not be implemented without the accurate Four Dimensional Trajectory Prediction (4D-TP). ...

To facilitate decision support in the air traffic management domain, an online four dimensional trajectory prediction (4D-TP) method was proposed in this paper. First, this study outlined the processes of online 4D-TP. Second, four major components of offline 4D-TP were discussed and presented, such as computation model, aircraft intent, environmental conditions and performance parameters. Third, this paper came up with an approach of current trajectory updating by using ADS-B Receiver and the corresponding data processing algorithm. Furthermore, the strategies of aircraft horizontal and vertical intent updating were also put forward for online 4D-TP. And the aircraft intent should be updated while the deviation between the current and predicted trajectory exceeding the pre-defined threshold. Finally, two types of case studies were carried out to demonstrate the performance and effectiveness of the proposed online 4D-TP method. The results indicated that the proposed online 4D-TP method is able to increase the prediction accuracy by triggering 4D-TP while the position or speed deviation is beyond the pre-defined threshold.

... 8 Stochastic programming and receding horizon control would be useful for this type of maneuver commanding. 9 Furthermore, an adaptive controller can be designed that senses when multiple thruster firings are necessary to reach the commanded rate . If the rate error consistently does not converge with multiple firings, the controller can update the lookup table accordingly. ...

Spacecraft control algorithms must know the expected vehicle response to any command to the available control effectors, such as reaction thrusters or torque devices. Spacecraft control system design approaches have traditionally relied on the estimated vehicle mass properties to determine the desired force and moment, as well as knowledge of the effector performance to efficiently control the spacecraft. A pattern recognition approach was used to investigate the relationship between the control effector commands and spacecraft responses. Instead of supplying the approximated vehicle properties and the thruster performance characteristics, a database of information relating the thruster firing commands and the desired vehicle response was used for closed-loop control. A Monte Carlo simulation data set of the spacecraft dynamic response to effector commands was analyzed to establish the influence a command has on the behavior of the spacecraft. A tool developed at NASA Johnson Space Center to analyze flight dynamics Monte Carlo data sets through pattern recognition methods was used to perform this analysis. Once a comprehensive data set relating spacecraft responses with commands was established, it was used in place of traditional control methods and gain sets. This pattern recognition approach was compared with traditional control algorithms to determine the potential benefits and uses.

... The runway scheduling problem has often an objective related to delay, makespan of the schedule, the number of changes in comparison with the First-come-first-served (FCFS) sequence, or various combinations. Approaches employed to solve this problem include hybrid tabu search (Atkin et al., 2007), dynamic programming (Balakrishnan and Chandran, 2006), branch and bound (Sölveling and Clarke, 2014) and genetic algorithms (Hu and Di Paolo, 2008). For a detailed review on this topic, see (Bennell et al., 2013). ...

In addition to time efficiency, minimisation of fuel consumption and related emissions has started to be considered by research on optimisation of airport surface operations as more airports face severe congestion and tightening environmental regulations. Objectives are related to economic cost which can be used as preferences to search for a region of cost efficient and Pareto optimal solutions. A multi-objective evolutionary optimisation framework with preferences is proposed in this paper to solve a complex optimisation problem integrating runway scheduling and airport ground movement problem. The evolutionary search algorithm uses modified crowding distance in the replacement procedure to take into account cost of delay and fuel price. Furthermore, uncertainty inherent in prices is reflected by expressing preferences as an interval. Preference information is used to control the extent of region of interest, which has a beneficial effect on algorithm performance. As a result, the search algorithm can achieve faster convergence and potentially better solutions. A filtering procedure is further proposed to select an evenly distributed subset of Pareto optimal solutions in order to reduce its size and help the decision maker. The computational results with data from major international hub airports show the efficiency of the proposed approach.

... Because the density of the flight, Ball et al. [15] reports that almost one of four airlines delays to their destination for 15 minutes from their target time in schedule in 2007. Additionally, Solveling and Clarke [14] say that one-third landing on latest time are caused by the direct traffic demand for exceeds the capacity of the aviation system. ...

... Two-stage stochastic linear problems are top-rated tools for tackling uncertainty and are applied in practice. Applications ranging from scheduling [2], finance [3], supply chain planning, and logistics [4], among others, are also described in [5]. In this context, decisions are made in stages according to when the values of stochastic parameters are revealed. ...

Benders Decomposition (BD) is a method used to solve stochastic linear problems via scenario analysis. Cluster BD (CBD) is one of its smart improvements that speed up the execution time, taking advantage of tighter feasible cuts found by grouping scenarios into clusters. In this paper, we propose a new design for CBD, one which takes into account the role played by optimal cuts in the solution. Besides, we propose a new parallel scheme for CBD to deal with large-scale two-stage stochastic linear problems. Moreover, we characterise the problems for which our proposal performs best. The results obtained show computational gains from our proposal compared with the plain use of CPLEX, serial BD, parallel BD, serial CBD and parallel CBD.

... Airport capacity management is one of the most frequently found topics in the literature on air transport management. It is discussed, for example, in [1], [6], [8], [9], [11], [20], [21]. These papers focus on various factors affecting airport capacity, e.g. ...

Increasing air traffic imposes the need to seek for solutions improving airport capacity. The standard approach is to expand the infrastructure. However, this is costly and time-consuming. This is why solutions increasing the capacity merely by changing the organization of aerodrome traffic are sought. The purpose of this paper is to present a new concept involving the optimization of braking on the runway. Standard braking profiles can be inefficient because of many possible disturbances and uncertainties. By applying the concept of infrastructure-to-vehicle communication it is possible to modify the standard braking profile so as to reach the desired speed in the vicinity of the runway exit and at the same time to not extend the runway occupancy time. Preliminary version of braking profile adjustment algorithm has been developed and implemented into the ACPENSIM simulator, built as hierarchical, coloured Petri net. Results for the simulation of the scenario where an aircraft touches down in a different place than it was planned and has a different mass, show the effectiveness of the algorithm. Modified braking profile allowed for achieving the appropriate final velocity with almost unchanged runway occupancy time, which determines the capacity of the airport.

... A 'first-come-firstserved' (FCFS) principle is accepted as a fair method of sequencing aircraft at most airports. In FCFS policy, aircraft are sequenced based on expected approach time (EAT) to a runway or a given point (43,44) . The results of the RTS analyses present that FCFS could be provided by implementing the LH procedure. ...

This study is aimed at establishing a linear holding (LH) procedure instead of a conventional air holding stack to minimize the effects of airborne delays in terms of air traffic management and fuel consumption. This paper uses both actual flight data and the Base of Aircraft Database (BADA) model to obtain fuel consumption for level flight and descent segments, separately.
The total fuel savings obtained by using actual flight data (16%) and the BADA model (10%) indicate that the LH is found to be more advantageous compared to a conventional holding procedure. Furthermore, the recommended LH procedure could be a promising solution for keeping aircraft in a narrow area that could be considered to be an effective method for airspace usage.

... For congested runways, re-arranging and optimizing the sequencing of runway 197 operations may leads to either a reduction in the number of aircraft in holding patterns or to an 198 increase in capacity, allowing for more landings per hour (Lieder et al., 2015). Figure it takes to complete a given set of operations (Sölveling and Clarke, 2014). For example, in Figure 205 3, four arrivals are considered, one heavy (H), two medium (M), and one light (L). ...

In this paper, we consider the aircraft landing problem of sequencing landings of aircraft of different types and sizes on a single runway. The objective is to determine the landing time within a specific time window per aircraft and the minimum allowable landing separation time between two consecutive aircraft. This is an NP-hard state-dependent scheduling problem. We present an efficient adapted heuristic model called closest aircraft sequence with time windows (CAS-TW). Our proposed greedy algorithm is inspired by the heuristic approaches to the travelling salesman problem (TSP) and combines tour constructive and insertion heuristics adapted with inviolable, hard constraints of time window and safety separations. Another characteristic of our model is that the first come, first served (FCFS) original order is respected, and the earliest aircraft in the original (FCFS) order is selected when two or more candidate solutions in the same permitted time window have the same pairwise distance. We used the Airland test case from the O-R Library benchmark problems and real data from the Sao Paulo-Guarulhos International Airport in our study to validate the effectiveness and efficiency of our proposed algorithm. We compared the results of our method with the FCFS and commercial mixed-integer programming (MIP) solver (CPLEX). The computational experiments reveal shorter makespans up to 21% in theoretical datasets and 5% in practical datasets. CAS-TW could solve instances with 50 aircraft using less than 1 second of computation time. The results showed that our algorithm was quickly implemented, equitable, easy to use, and obtained good solutions. It was quickly implemented because the proposed solutions were available in a very short time; it was equitable because it deviated little from the FCFS order; it was easily coded; and its solutions were better than the FCFS solution and similar or better than the optimal MIP solution obtained with CPLEX for a given computational time limit. Consequently, these results translated into an increase in airport capacity.

... Pioneer studies of the ALP considering uncertainty were conducted by [34,9], and [32] who basically added probabilistic considerations to the deterministic ALP. Stochastic optimization models, including two-stage and multi-stage models, were applied by [42,40,41], and [7] to address a variant of the ALP under uncertainty that considers departures and surface operations on the airport. Recently, [23,26], and [22] proposed various robust optimization models to address the runway scheduling problem under uncertainty. ...

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

... Because of capacity problems, there is a growing need for changes in the air traffic system to accommodate the increase in demand for air traffic (Hu and Chen, 2005). Congestion in the terminal area (TMA) composes a considerable part of all flight delays for arriving aircraft (Sölveling and Clarke, 2014). Arrival runways are strategic at an airport. ...

Delay is a key point in air transportation activity. As a performance metric, it affects common policy concerns. Delay impacts passenger satisfaction and imposes costs. The complexity that sets in for the air traffic manager is how to mitigate delay, especially in an environment with several stakeholders. The present article applied a problem-structuring method (PSM), named value-focused thinking (VFT), to structure the problem of the air traffic flow management arrival delay. The inflexibility of incorporating a flight operator's specific needs is considered one of the reasons for the limited success of air traffic flow management (ATFM) programs. PSM allows participants to clarify their dilemmas , converge on a mutually liable problem, or agree to the proposed solutions and compromise on what partially solves the issue. The problem is that most papers focus only on the applied solution for air delay mitigation. Before implementing operational research techniques, we investigated the nature and characteristics of air delay. Results showed that there were several stakeholders with distinctive requirements for their business and many of their objectives are interconnected. The use of VFT provided an objective map that can be used as a guide for future solutions.

... Many research efforts have been made to tackle the ASS problem, both from the perspective of modeling the problem (Beasley et al. 2000(Beasley et al. , 2001(Beasley et al. , 2004Dear 1976;Psaraftis 1978Psaraftis , 1980, as well as developing various optimization approaches for solving it, including mathematical programming (Faye 2015;Lieder et al. 2015;Ma et al. 2014;Sölveling and Clarke 2014;Tavakkoli-Moghaddam et al. 2012) and heuristic algorithms (Guo et al. , 2009Jia et al. 2008;Tang et al. 2008;Wang et al. 2008;Yu et al. 2011). As early as 1978, a simplified version of the ASS is investigated, in which all the flights are supposed to land immediately and the flights with the same type are considered to be equivalent. ...

Aircraft arrival sequencing and scheduling is a classic problem in the air traffic control to ensure safety and order of the operations at the terminal area. Most of the related studies have formulated this problem as a static case and assume the information of all the flights is known in advance. However, the operation of the terminal area is actually a dynamic incremental process. Various kinds of uncertainties may exist during this process, which will make the scheduling decision obtained in the static environment inappropriate. In this paper, aircraft arrival sequencing and scheduling problem is tackled in the form of a dynamic optimization problem. An evolutionary approach, namely dynamic sequence searching and evaluation, is proposed. The proposed approach employs an estimation of distribution algorithm and a heuristic search method to seek the optimal landing sequence of flights. Compared with other related algorithms, the proposed method performs much better on several test instances including an instance obtained from the real data of the Beijing Capital International Airport.

... Airport capacity management is one of the most frequently found topics in the literature on air transport management. It is discussed, for example, in Irvine et al. (2015), Gelhausen et al. (2013), Kalakou et al. (2014), Farhadi et al. (2014, Sölveling and Clarke (2014), Stelmach et al. (2006) and Balakrishna et al. (2010). These papers focus on various factors affecting airport capacity, e.g. ...

... The simulation results to validate the proposed algorithm are also provided. Solveling and Clarke (2014) addressed the stochastic version of the problem in which a set of aircraft are to be scheduled on one or multiple dependent runways. They developed a two-stage stochastic integer program and a solution method using scenario decomposition based on Lagrangian relaxation. ...

Even a moderately sized real-life runway scheduling problem tends to be too complex to be solved by analytical methods where the proposed mathematical models for this problem all belong to the complexity class of NP-Hard in a strong sense. Therefore, it is only possible to solve practical runway scheduling problems using mathematical programming methods by making a large number of simplifications and assumptions. As a result, most of the analytical models proposed in the literature suffer from too much abstraction and, in turn, not much applicability in practice. However, simulation-based methods have the capability to characterize complex and stochastic real-life runway systems in detail, as well as cope with several constraints and multiple objectives, which are important factors in practice. With a simulation-based optimization (SbO) approach where a discrete event simulation model is integrated with an optimization algorithm, the search for Pareto-optimal solutions can be done conveniently. Due to its large and unstructured search space, finding exact Pareto-optimal solutions to such multi-objective optimization problem is computationally intractable; given that such solutions need to be found in a reasonable timeframe, metaheuristic algorithms are the best option to pursue. In this study, a hybrid metaheuristic algorithm based on scatter search (SS), which takes advantage of the structural details of the problem, and uses a dynamic update mechanism to produce high-quality solutions and a rebuilding strategy to promote diversity, is proposed and presented. SS-based multi-objective evolutionary algorithms seem to be a promising research direction due to its efficiency and effectiveness in finding a set of non-dominated solutions in a SbO framework with multiple objectives. The experimental results that evaluate the proposed hybrid metaheuristic algorithm's performance in terms of both diversity of solutions and their proximity to the Pareto frontier are also presented.

... In many optimization problems (including discrete optimization), arbitrarily small errors in the specification of the input data may lead to significant changes in the true solution [15], [16]. An approach to address the uncertainties in the arrival sequence of the aircraft is to exploit stochastic optimization techniques [4], [17], [18]. These typically require information about the nature of the uncertainty and arrive at a solution that optimizes the expected value of a performance metric. ...

By performing stability analysis on an optimal runway schedule, this paper derives a method to determine whether an optimized landing sequence of aircraft remains optimal after an arbitrary number of aircraft in that sequence are delayed by an arbitrary amount of time. We consider the problem of scheduling aircraft landing on a single runway with the objective of maximizing throughput under changing external conditions such as delays caused by weather. Instead of optimizing the schedule every time delays occur, stability criteria allow for fast evaluation of whether schedules remain optimal. This paper develops a method to compute stability regions for a set of schedules. Sensitivity analysis of the linear programming relaxation and a nonlinear relationship between the delay of individual aircraft and the incurred cost change for all landing sequences yield the stability information. Furthermore, the properties of a first-come–first-serve policy are studied by giving sufficient conditions and a heuristic condition for the optimality of first-come–first-serve sequences. The given results are shown to be also applicable to landing sequences obtained through local neighborhood search, sequences that obey a position shift constraint, and subsequences of landing sequences as used in a rolling horizon approach.

... For instance, Wei etc. [21] revealed the optimal relationship between traffic stream characteristics, operation mode of each runway and flight scheduling to simultaneously minimizing flight delays and maximizing runway utilization. Further, these studies for both FS-SR and FS-MR could be classified as static or dynamic, where static FS schedules landing/departing flights in a static environment to these runways in advance [6,22,23] and dynamic FS reschedules an incomplete set of landing/departing flights in a dynamic environment to runways using the First in First Out (FIFO) rule [11,14,24,25]. For instance, Zhang etc. [25] established an arrival sequencing model was by introducing the concept of alternative approach routes and time-deviation cost. ...

This paper presents an optimization model for assigning a set of arrival and departure flights to multiple runways and determining their actual times with consideration of incursions. Due to the lack of data, fuzzy incursion time is used to describe the uncertainty with the help of artificial experience. Moreover, the multiple-goal priority considerations of air traffic controllers are also fully considered in this model. The two objectives are to simultaneously minimize delays in arrival and departure flights. Since this problem is NP-hard, a novel polynomial algorithm based on queuing theory is also proposed to obtain acceptable solutions efficiently. Finally, a real-world example is provided to analyze the effect of different times and places of incursion events on the scheduling scheme, which can verify the correctness of the model. Results show that higher runway incursion times lead to longer queue lengths for take-off and landing flights, resulting in more flight delays.

... Regarding calculation environments, some studies set the problem scenarios to static [5] and others were carried out in a dynamic context [7]. For solution algorithms, in terms of small-scale ALP, the problem is formulated as a mixed-integer linear programing (MILP), and CPLEX was used to solve it [8]; in terms of large-scale ALP, dynamic programming (DP) [9], branch and bound (BB) [10], heuristic algorithms [11], and meta-heuristic algorithms including genetic algorithm (GA) [12], simulated annealing (SA) algorithms [13], and particle swarm optimisation (PSO) [14] were implemented. As to optimisation objectives that appeared in previous studies, they were not the same and were presented as the following: (1) minimising the total penalty [8,9,13,14]; (2) minimising the total delay [12,15]; and (3) minimising the last flight's landing time, or maximising the throughput of runway [16]. ...

The arrival management (AMAN) system is a decision support tool for air traffic controllers to establish and maintain the landing sequence for arrival aircraft. The original intention of designing the AMAN system is to improve the efficiency of air traffic management (ATM), but few studies are investigating the operational benefits of this system based on key performance indicators (KPIs) and evaluating actual data in a real-time environment. The main purpose of this paper is to propose a KPI based transferable comparative analysis method for identifying the operational benefits of the AMAN through radar trajectories. Firstly, six KPIs are established from a joint study of the mainstream ATM performance frameworks worldwide. Secondly, appropriate evaluation technique approaches are determined according to the characteristics of each KPI. Finally, a Chinese metropolitan airport is taken for the case study, and three periods are defined to form data samples with high similarity for comparative experiments. The results validate the feasibility of the proposed method and find comprehensive performance improvements in arrival operations under the effects of the AMAN system.

... Many researchers have taken this algorithm as a tool to develop papers in areas of knowledge such as the problem of the traveling salesman [29], to determine locations [30], to solve problems of operations in airports [31,32], the use of resources in case of need [33], and plan spatial missions [34]. ...

The ordered weighted averaging (OWA) operator is one of the most used techniques in the operator’s aggregation procedure. This paper proposes a new assignment algorithm by using the OWA operator and different extensions of it in the Branch-and-bound algorithm. The process is based on the use of the ordered weighted average distance operator (OWAD) and the induced OWAD operator (IOWAD). We present it as the Branch-and-bound algorithm with the OWAD operator (BBAOWAD) and the Branch-and-bound algorithm with the IOWAD operator (BBAIOWAD). The main advantage of this approach is that we can obtain more detailed information by obtaining a parameterized family of aggregation operators. The application of the new algorithm is developed in a consumer decision-making model in the city of Barcelona regarding the selection of groceries by districts that best suit their needs. We rely on the opinion of local commerce experts in the city. The key advantage of this approach is that we can consider different sources of information independent of each other.

... This formulation is acknowledged as one of the most classic models in the field of ASS research. Therefore, many research efforts on the mathematical programming have been made to solve this problem [43,49,51,53,54]. Although mathematical programming also has great universality, its relatively low efficiency will become the greatest performance bottlenecks of this method, especially used to solve a large-scale problem. ...

Arrival sequencing and scheduling (ASS) is an important part of air traffic control. In the literature, various formulations of the ASS problems have been established by taking different scheduling requirements into account, and various methods have been developed to cope with these ASS problems. However, it is usually uneasy to generalize a method designed for one ASS formulation to another, while an approach that is able to handle different ASS problems is of great significance since air traffic controllers may need to switch among different scheduling requirements in practice. Motivated by this observation, an approach that is applicable to a number of different problem formulations of ASS is proposed in this paper. Specifically, the ASS problems that include different objective functions and constraints are firstly abstracted as a constrained permutation-based problem. After that, a Sequence Searching and Evaluation (SSE) approach is developed for the constrained permutation-based problem. The SSE solves different ASS problems by separating the sequence searching in one stage using an Estimation of Distribution Algorithm framework, and evaluating sequences in the second stage. Experiment results show that SSE is capable of obtaining competitive solutions for a variety of ASS problems.

... An overview can be found in the study of Kwasiborska & Skorupski (2014). Sölveling & Clarke (2014) developed an algorithm for the determination of an optimal (or close to optimal) solution of the stochastic operation sequencing problem. It works for one or more runways while minimizing the difference between the begin and the end time of the task sequence. ...

The organization of traffic in the vicinity of transportation network nodes is a major challenge for traffic management services. It is essential to ensure the safety of moving vehicles, in air transport achieved through the use of appropriate separation between aircraft. In recent years, however , growing emphasis is on providing high throughput, which is particularly important due to the ever increasing traffic. Existing methods for supporting traffic management are evolving in the direction of increasing the planning horizon and the early formation of traffic streams. In air transport, it takes the form of Arrivals Management (AMAN), which is one of the key objectives for the SESAR project— technological part of the concept of the Single European Sky program. The result of the process of arrivals management is the sequence of aircraft, taking into account not only their order but also the time of appearance in the relevant navigation waypoints. In this paper we analyze the problem of reliability assessment of the traffic flow management process. In the case of sequence of aircraft separated by a small time interval we may expect the high capacity of the airport, but it is likely that, because of the need to maintain the safety, the sequence will be distorted and will not be possible to realize. Introduction of an additional time buffer between aircraft has the opposite effect. Our paper presents a mathematical model and a computer tool allowing for the evaluation of the traffic flow management process in case of random disturbances, which may be subject to aircraft. Particular attention is paid to disturbances that can be partially predicted. The algorithm for compensation of this type of interference in the aircraft arrivals planning process is proposed.

... Aviation management has received great attention in the literature to enhance operations efficiency and reduce associated costs. Several management areas have been investigated, such as ground holding Andreatta et al. (1993); Brunetta et al. (1998); Mukherjee and Hansen (2007), gate assignment Bihr (1990); Cheng et al. (2012); Ding et al. (2005), runway sequencing and scheduling Bennell et al. (2013); Atkin et al. (2007); Ikli et al. (2021); Sölveling and Clarke (2014), conflict resolution Alonso-Ayuso et al. (2014); Menon et al. (1999); Pallottino et al. (2002); Peyronne et al. (2015), airspace capacity management Barnhart et al. (2012); Liu and Hu (2009) ;Sherali and Hill (2013), and air traffic flow management Boujarif et al. (2021b). An air traffic flow management problem (ATFM) involves optimizing flight schedules to match schedules with the available airport and airspace capacities Bertsimas and Patterson (1994). ...

We discuss a widely used air traffic flow management formulation. We show that this formulation can lead to a solution where air delays are assigned to flights during their take-off which is prohibited in practice. Although air delay is more expensive than ground delay, the model may assign air delay to a few flights during their take-off to save more on not having as much ground delay. We present a modified formulation and verify its functionality in avoiding incorrect solutions.

... The ALP has been studied widely, and detailed literature reviews have been presented [3][4][5]. The exact solution approaches employed in the ALP are given as follows: CPLEX solver [6][7][8][9][10][11], dynamic programming [12][13][14][15][16][17], and branch and bound (B&B) algorithm [18][19][20] have been applied as exact solution algorithms. Samà et al. [5] presented a mixed-integer linear programming (MILP) model for the aircraft scheduling problem with different objective functions. ...

This study presents a mathematical model to optimize the total fuel consumption per aircraft for the aircraft landing problem (ALP) using the path stretching (PS) method. The PS model applies vector maneuver (VM), speed reduction (SR), and flight path angle (FPA) change methods for aircraft operation. In addition, two different mixed-integer linear programming models utilizing the point merge system (PMS) are presented to compare the PS model as PMS is a widely used method in ALP. The first PMS model uses the VM to handle arrival traffic and solve aircraft conflicts. The second one implements the VM and the SR techniques. Furthermore, an exact solution algorithm is selected to obtain the optimal solution. The PS model aims to increase the number of continuous descent operations by eliminating the level flights. Two different linear regression equations are generated to calculate the fuel consumption and flight time values in descent operations considering realistic aircraft parameters, FPA, and average airspeed. The results demonstrate that the PS model can reduce the total fuel consumption per aircraft by 8.94% and 3.45% compared to the PMS models.

One of the important tasks that air traffic management services are faced with today is the task of maximizing airport capacity. This can be achieved at the tactical level through proper organization of air traffic around an airport. In recent years many methods and algorithms for scheduling aircraft landings have been developed; they take into account various optimization goals. The aim of this paper was to create a method that would allow one to evaluate landing aircraft sequences resulting from these control algorithms, especially in the presence of random disturbances. This method involves modeling the landing aircraft sequence by using Petri nets. The model and the computer tool that have been developed make it possible to take into account different kinds of disturbances and examine the effectiveness of various control strategies under these conditions. This paper presents two experiments that test disturbances with different characteristics and of different intensities. It has been shown that small but more frequent disturbances lead to the worsening of evaluation scores for a given sequence to a lesser extent than rare but larger disturbances. This is particularly important for control algorithms in which the focus is on high aircraft density. If the type of particular disturbances is properly assessed then it will be possible to assist the decision-maker (air traffic controller) by providing quantitative evaluations of possible solutions to him/her.

We present an alternative approach to the problem of periodic crew scheduling. We introduce the concept of frames which leads us to a modeling approach which suits well the current practice of the majority of European railway operators. It results in a model facilitating column generation techniques resulting in a Dantzig-Wolfe type decomposition, and thus suitable for a parallel implementation in a high-performance computing environment. We exploit the properties of network flow models to avoid several additional integer constraints. We compare two approaches to solve the problem. The first approach consists of solving the original problem by single model. The second approach is our step-by-step column generation. The comparison is based on our implementation which we describe in detail along with its application to certain benchmark instances. The benchmarks originate in real or close-to-realistic problems from railway systems in Slovakia and Hungary. The case studies demonstrate that our model is well-suited for real-life applications.

Organizacja ruchu w rejonach lotnisk jest jednym z trudniejszych zadań dla służb zarządzania ruchem lotniczym. Wynika to z dużej liczby samolotów wykonujących skomplikowane manewry w ograniczonej przestrzeni ruchowej. Jednym z kluczowych procesów występujących w tym obszarze jest szeregowanie samolotów lądujących. Celem artykułu jest przedstawienie koncepcji implementacji systemu służącego do oceny tego procesu. Metoda oceny opiera się na wyznaczeniu liczby lądowań możliwych do zrealizowania przy danym uszeregowaniu w jednostce czasu. Na podstawie przeprowadzonych pomiarów ruchu lotniczego przeanalizowano rzeczywiste uszeregowania stosowane w praktyce. Pokazuje ona, że wykorzystywane w praktyce przez kontrolerów ruchu lotniczego algorytmy szeregowania pozwalają na znacznie mniejszą liczbę lądowań w jednostce czasu, niż wynikałoby to z przepisów. Wskazuje to na istnienie dużego potencjału w ramach wdrażania systemów wspomagania kontrolera w procesie szeregowania samolotów lądujących.
Traffic organization in the airport area is one of the most difficult tasks for air traffic management services. This is due to the large number of aircraft performing complicated maneuvers in limited airspace. One of the key processes occurring in this area is the scheduling of landing aircraft. The aim of this study is to present the concept of implementation of a system for the evaluation of this process. The assessment method is based on determining the number of viable landings per unit time at a given aircraft schedule. On the basis of real air traffic measurements real landing aircraft schedules were analyzed. This shows that algorithms used by air traffic controllers in practice allow for a much smaller number of landings per unit of time than would result from the regulations. This indicates the existence of a large capacity to implement controller support systems in the process of aircraft landing scheduling.

Nowadays, the problem of creating an optimal safe schedule for arrival of aircraft coming in several flows to a checkpoint, where these flows join into one, is very important for air-traffic management. Safety of the resultant queue is present if there is a safe interval between neighbor arrivals to the merge point. Change of an arrival instant of an aircraft is provided by changing its velocity and/or usage of fragments of the air-routes scheme, which elongate or shorten the aircraft path. Optimality of the resultant queue is considered from the point of some additional demands: minimization of the deviation of the actual aircraft arrival instant from the nominal one, minimization of order changes in the resultant queue in comparison with the original one, minimization of fuel expenditures, etc. The optimality criterion to be minimized, which reflects these demands, is often taken as a sum of penalties for deviations of the assigned arrival instants from the nominal ones. Each individual penalty is considered in almost all papers as either the absolute value of the difference between the assigned and nominal arrival instants or a similar function with asymmetric branches (which punishes delays and accelerations of an aircraft in different ways). The problem can be divided into two subproblems: one is a search for an optimal order of aircraft in the resultant queue, and the other is a search for optimal arrival instants for a given order. The second problem is quite simple since it can be formalized in the framework of linear programming and solved quite efficiently. However, the first one is very difficult and now is solved by various methods. The paper suggests sufficient conditions for the problem, which guarantee that the order of the optimal assigned instants is the same as the order of the nominal ones and, therefore, exclude the first subproblem.

This work aims to minimize the waiting time in the runway queue, by proposing a non-iterative real-time model, which can assist air traffic controllers in decision making in times of congestion on the ground at any airport. The model shows that the number of sequenced aircraft at the same time directly influences waiting times and makespan. In addition, factors such as landing time and operational restrictions modify the optimized sequencing as well as the waiting time of the aircraft on the ground. Particularly, the separation minima possibly become the major factor of influence when the SID is considered. Finally, by using Monte Carlo simulation it was possible to state that uncertainties related to taxiing time do not imply significant changes in the departure queue.

The purpose of this review is to present the literature base of airport disaster management (ADM) for non-aviation related events. This study systematically reviews the recent literature to report ADM efforts, identify gaps for future research and determine related research questions to be addressed. In this study, Systematic Literature Review (SLR) approach proposed by Denyer and Tranfield (2009) was used. Transparency, audibility and replicability are the main objectives of this SLR. The studies which were published within the period 2007 and 2017 were reviewed. The papers were screened in the academic databases such as Wiley, Emeraldinsight, ScienceDirect, SpringerLink, Google scholar and Taylor & Francis. However, papers which are related to the research aim were only found in Emeraldinsight, ScienceDirect, SpringerLink and Google Scholar. Twenty-three papers were analyzed including peer reviewed articles and theses. As a result of the review, it was determined that the previous studies mainly focused on five research topics such as stakeholder collaboration, scheduling problems, medical preparedness, infrastructure planning and corporate social responsibility. The study is considered as original in the sense that it is the first systematic research that investigates disaster management for non-aviation related conditions in airport setting.

Allocating efficient routes to taxiing aircraft, known as the Ground Movement problem, is increasingly important as air traffic levels continue to increase. If taxiways cannot be reliably traversed quickly, aircraft can miss valuable assigned slots at the runway or can waste fuel waiting for other aircraft to clear. Efficient algorithms for this problem have been proposed, but little work has considered the uncertainties inherent in the domain. This paper proposes an adaptive Mamdani fuzzy rule based system to estimate taxi times and their uncertainties. Furthermore, the existing Quickest Path Problem with Time Windows (QPPTW) algorithm is adapted to use fuzzy taxi time estimates. Experiments with simulated taxi movements at Manchester Airport, the third-busiest in the UK, show the new approach produces routes that are more robust, reducing delays due to uncertain taxi times by 10–20% over the original QPPTW.

The arrival manager operational horizon, in Europe, is foreseen to be extended up to 500 n miles around destination airports. In this context, arrivals need to be sequenced and scheduled a few hours before landing, when uncertainty is still significant. A computational study, based on a two-stage stochastic program, is presented and discussed to address the arrival sequencing and scheduling problem under uncertainty. This preliminary study focuses on a single initial approach fix and a single runway. Different problem characteristics, optimization parameters, as well as fast solution methods for real-time implementation are analyzed in order to evaluate the viability of our approach. Paris Charles-De-Gaulle airport is taken as a case study. A simulation-based validation experiment shows that the current approach can decrease the number of expected conflicts near the terminal area by up to 70%. Moreover, in a high-density traffic situation, the total time to lose inside the terminal area can be decreased by more than 71%, whereas the expected landing rate can be increased by 7.7% as compared to the first-come/first-served policy. This computational study demonstrates that sequencing and scheduling arrivals under uncertainty a few hours before landing can successfully diminish the need for holding stacks by relying more on upstream linear holding.

Aircraft landing is a critical operation for both terminal airspaces and airports. This study presents a multi-objective optimization model for this problem and aims to minimize the total flight time and emission value. A point merge system and vector maneuver techniques are implemented in aircraft to regulate air traffic. The model uses the augmented è-constraint method to reveal objective function relationships. To test the performance of the mathematical model, several realistic scenarios are generated and solved by GAMS/CPLEX solver. The algorithm can obtain Pareto-optimal solutions for each air traffic situation. In addition, noticeable reductions were observed in most of the Pareto-optimal solutions in emission values. The results showed that total emissions value and flight time were reduced up to 4.69% and 0.92%, respectively, compared with the first-come-first-served approach.

Aircraft sequencing and scheduling within terminal airspaces has become more complicated due to increased air traffic demand and airspace complexity. A stochastic mixed-integer linear programming model is proposed to handle aircraft sequencing and scheduling problems using the simulated annealing algorithm. The proposed model allows for proper aircraft sequencing considering wind direction uncertainties, which are critical in the decision-making process. The proposed model aims to minimise total aircraft delay for a runway airport serving mixed operations. To test the stochastic model, an appropriate number of scenarios were generated for different air traffic demand rates. The results indicate that the stochastic model reduces the total aircraft delay considerably when compared with the deterministic approach.

Runway systems are among the most stringent bottlenecks at global hub airports, which have been identified as a major source of airport inefficiency. Runway system inefficiencies are manifested in multiple dimensions such as delay, throughput reduction and excessive emission, whose tradeoffs are investigated in this paper as part of an airport runway scheduling problem in the presence of uncertainty. We formulate a multi-objective optimization model aiming to minimize flight delays, maximize airport throughput, and minimize aircraft emissions, subject to a variety of constraints such as minimum separation, time window, runway occupancy and flight turnaround. The computational performance is enhanced with an efficient multi-objective evolutionary algorithm, with two mechanisms of adaptive and controllable time-coding and objective-guided individual selection. The proposed method is flexible in adjusting conservatism when it comes to optimization with uncertainty, and offers a set of Pareto optimal solutions for different stakeholders without using scalarization of different objectives. A real-world case study is carried out for one of the world’s buiest airports, Shanghai Pudong, under the case of 2 runways, 2 operation types, 12 uncertain conditions and 4 tradeoff scenarios. The computational results show that the proposed optimized method has overall advantages in improving the runway scheduling performance over some meta-heuristics and the First Come First Served strategy. The tradeoff analysis reveals that the minimum delay schedule is preferable for balancing delay, throughtput and emission. The findings provide managerial insights regarding traffic management measures for different stakeholders at high-density airports.

The organization of landing operation and related issues within an Air Traffic Control (ATC) system in the airport Terminal Maneuvering Area (TMA) are hitherto performed by human air traffic controllers. These latter skilled buffers are responsible for aligning and controlling a continuous inbound flow of aircraft. These tasks are beginning from the time of notification of the getting of arrivals to the TMA entry fixes until the end of landings on the assigned runway(s). The whole duties carried out by air traffic controllers, such as arrival control, sequencing, scheduling, and assignment solutions are frequently implemented according to the information shown on various instruments, and some simple rules such as First Come First Served (FCFS) discipline. It is also worth noting that the training and past experience of the air traffic controllers are playing a leading role, and are essential part of decision-making processes. Since the demand for air traffic has continued to rise and with the emergence of congested airports, it became clear that the mission entrusted to the air traffic controller and its ability to undertake in its job in the right way has become increasingly more exacting. Consequently, there has been a greater demand to make the ATC more automated by improving aircraft scheduling/sequencing techniques, and developing further decision support systems, to which the challenge intends to alleviate the human intervention and not to replace the air traffic controller. Here of, the core goal is to provide a system review of past and the most up-to-date research related to the Aircraft Landing Problem (ALP) for an airport, which may include a single or multiple runways. Recognizing that the theoretical aspect relating to the ALP is dealt with this study, the evaluation of several solutions for that specific problem is furthermore covered. This evaluation will not succeed without explaining first the landing operation from a practical standpoint, which is a fundamental way to better understand the reasons why research effort has been devoted to suggest solutions for the overall arrival management. A comparative study which selects the distinguishing features that can be recognized in some research works against other related works is then proposed. In the last, a summary of the findings of published literature and recommendations for the future trend of ALP are pointed up as conclusions.

Existing research about the maintenance optimisation of production systems with intermediate buffers largely assumed a series system structure. However, practical production systems often contain subsystems of ring structures, for example, rework and feedforward. The maintenance optimisation of these complex systems is difficult due to the complicated structure of maintenance policies and the large search space for optimisation. This paper proves the control limit property of the optimal condition-based maintenance policy. Based on the control limit property, approximate policy structures that incur a smaller policy space are proposed. Because the state space of a production system is often large, the objective function of the maintenance optimisation cannot be evaluated analytically. Consequently, a stochastic branch and bound (SB&B) algorithm embedding a sequential simulation procedure is proposed to determine a cost-efficient condition-based maintenance policy. Numerical studies show that the proposed maintenance policy structures can deliver a cost-efficient maintenance policy, and the performance of the SB&B algorithm is enhanced by the inclusion of a sequential simulation procedure.

Complex projects, such as product development projects, usually involve myriads of interrelated activities. Identifying an appropriate sequence of these activities is a challenge to project managers because of the existence of rework iterations. Researchers have developed a series of methods to find a schedule that minimizes the first-order rework of interrelated activities using the design structure matrix (DSM). By contrast, this study presents a more accurate approach for determining a sequence that minimizes the high-order rework. First, a new objective function is proposed to describe the first-order and second-order rework time (FSRT) of complex projects. Second, a parallel branch-and-prune algorithm and two local search heuristics are proposed, which can be conveniently used to reduce the FSRT. Experimental results show that we can reduce more rework of complex projects through minimizing FSRT than using other objective functions. Finally, the efficiency of the proposed methods is validated using random experiments.

This study proposes a new operational concept of the Point Merge System, called Multi-Arrival Route Point Merge System (MAR-PMS), which is an air traffic control method used to sequence aircraft arrivals in a given terminal control area. The proposed concept enables the additional arrival routes that have an angular difference to each sequencing leg. Furthermore, a time-indexed 0-1 linear programming model is formulated. The obtained results are validated in a real time simulation. The comparison results of PMS and MAR-PMS show that the average reduction of 19% of total flight time, 23% of total flight distance, and 19% in total fuel burned and reduction in CO 2 emissions in favor of a proposed concept.

This study considers the terminal traffic flow problem and aims to minimize the total fuel consumed in extended terminal maneuvering areas (E-TMA) using a mixed-integer linear programming model. To reveal the benefits of the E-TMA concept, the exact solution solver is selected to determine optimal aircraft sequencing. Furthermore, the proposed model applies separation and sequencing maneuvers, including the point merge system (PMS), vector maneuvers (VM), and en route speed reduction maneuvers. An innovative mathematical model is presented for this problem. In this study, the proposed model is compared with two other approaches. The first uses VM and PMS without changing the initial sequencing. The second utilizes the VM and PMS maneuvers. Unlike the first approach, it searches for the optimum aircraft arrival sequencing. The results demonstrate that the proposed model could reduce total fuel consumption by 9.45% and 1.95% compared with the other two approaches.

This study presents a stochastic mixed-integer linear programming model for the aircraft sequencing and scheduling problem. The proposed model aims to minimise the average fuel consumption per aircraft in the Terminal Manoeuvring Area while considering uncertain flight durations for each flight. The tabu search algorithm was selected to solve the problem. The stochastic solution and deterministic solution results were compared to show the benefits of the stochastic solution. The average sample approximation technique was applied to this problem, and enhancement rates of the average fuel consumption per aircraft were 8.78% and 9.11% comparing the deterministic approach

Extended aircraft arrival management under uncertainty has been previously studied in the literature using two-stage stochastic optimization in the case of a single initial approach fix (IAF) and a single runway. In this paper, we propose an extension taking into account: (i) multiple IAFs feeding the landing runway, (ii) aircraft having different initial flight status (at-departure-gate or airborne) when making first-stage decisions, and (iii) a time-deviation cost function to minimize that is based on reference values depending on aircraft type and flight phase. Two problem variants are modeled according to the degree of freedom on IAF assignment to aircraft. In the first variant, IAFs are to be assigned to aircraft, as a first-stage decision. In the second variant, IAF assignment is fixed and considered as a problem input. Numerical results on realistic instances from Paris Charles-de-Gaulle airport confirm the benefit of taking into account uncertainty through two-stage stochastic programming, and through re-assignment of IAFs.

A mixed integer linear program is presented for deterministically scheduling departure aircraft at runways. The method addresses different schemes of managing the departure queuing area by treating it as first-in-first-out queues or as a simple parking area, where any available aircraft can take-off irrespective of its relative sequence with others. The method explicitly considers separation criteria between successive departures and also incorporates an optional prioritization scheme using time windows. Multiple objectives pertaining to throughput, system delay and maximum individual delay are used. Results indicate minimizing system delay alone improves throughput over a basic first-come-first-serve rule. Modifications for computational efficiency are also presented in the form of re-formulating certain constraints and defining additional inequalities for better bounds.

Active runway scheduling involves scheduling departures for takeoffs and arrivals for runway crossing subject to numerous constraints. This paper evaluates the effect of uncertainty on a deterministic runway scheduler. The evaluation is done against a first-come-first-serve scheme. In particular, the sequence from a deterministic scheduler is frozen and the times adjusted to satisfy all separation criteria; this approach is tested against FCFS. The comparison is done for both system performance (throughput and system delay) and predictability, and varying levels of congestion are considered. The modeling of uncertainty is done in two ways: as equal uncertainty in availability at the runway as for all aircraft, and as increasing uncertainty for later aircraft. Results indicate that the deterministic approach consistently performs better than first-come-first-serve in both system performance and predictability.

Due to an anticipated increase in air traffic during the next decade, air traffic control in busy airports is one of the main challenges confronting controllers in the near future. Since the runway is often a bottleneck in an airport system, there is great interest in optimizing usage of the runway. Our study first presents a brief review of the aircraft landing problem. A model for the problem is then introduced, and possible solution approaches are discussed.

A Dynamic Programming approach for sequencing a given set of jobs in a single machine is developed, so that the total processing cost is minimized. Assume that there are N distinct groups of jobs, where the jobs within each group are identical. A very general, yet additive cost function is assumed. This function includes the overall completion time minimization problem as well as the total weighted completion time minimization problem as special cases. Priority considerations are included; no job may be shifted by more than a prespecified number of positions from its initial, First Come-First Served position in a prescribed sequence. The running time and the storage requirement of the Dynamic Programming algorithm are both polynomial functions of the maximum number of jobs per group, and exponential functions of the number of groups N.

A mixed integer linear program is presented for deterministically scheduling departure and arrival aircraft at airport runways. This method addresses different schemes of managing the departure queuing area by treating it as first-in-first-out queues or as a simple parking area where any available aircraft can take-off irrespective of its relative sequence with others. In addition, this method explicitly considers separation criteria between successive aircraft and also incorporates an optional prioritization scheme using time windows. Multiple objectives pertaining to throughput and system delay are used independently. Results indicate improvement over a basic first-come-first-serve rule in both system delay and throughput. Minimizing system delay results in small deviations from optimal throughput, whereas minimizing throughput results in large deviations in system delay. Enhancements for computational efficiency are also presented in the form of re-formulating certain constraints and defining additional inequalities for better bounds.

A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic
case, the feasible set is partitioned into compact subsets. To guide the partitioning process the method uses stochastic upper
and lower estimates of the optimal value of the objective function in each subset. Convergence of the method is proved and
random accuracy estimates derived. Methods for constructing stochastic upper and lower bounds are discussed. The theoretical
considerations are illustrated with an example of a facility location problem.

. Many applications such as project scheduling, workflow modeling or business process re-engineering incorporate the common idea that a product, task or service consisting of interdependent time--related activities should be produced or performed within given time limits. In real applications, certain measures like extra manpower, assignment of highly--skilled personnel to specific jobs or substitution of equipment are often considered in order to increase the probability of meeting the due date and thus avoiding penalty costs. This paper investigates the problem of selecting, from a set of possible measures of this kind, the combination of measures that is the most cost--efficient. Assuming stochastic activity durations, the computation of the optimal combination of measures may be very expensive in terms of runtime. In this article we introduce a powerful stochastic optimization approach to determine a set of efficient measures that crash selected activities in a stochastic activit...

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 separation criteria between the landing of a plane, and the landing of all successive planes, are respected. We present a mixed-integer zero-one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming based tree search. We also present an effective heuristic algorithm for the problem. Computational results for ...

This paper addresses the challenge of building an automated decision support methodology to tackle the complex problem faced
every day by runway controllers at London Heathrow Airport. Aircraft taxi from stands to holding areas at the end of the take-off
runway where they wait in queues for permission to take off. A runway controller attempts to find the best order for aircraft
to take off. Sequence-dependent separation rules that depend upon aircraft size, departure route and speed group ensure that
this is not a simple problem to solve. Take-off time slots on some aircraft and the need to avoid excessive delay for any
aircraft make this an even more complicated problem. Making this decision at the holding area helps to avoid the problems
of unpredictable push-back and taxi times, but introduces a number of complex spatial constraints that would not otherwise
exist. The holding area allows some flexibility for interchange of aircraft between queues, but this is limited by its physical
layout. These physical constraints are not usually included in academic models of the departure problem. However, any decision
support system to support the take-off runway controller must include them. We show, in this paper, that a decision support
system could help the controllers to significantly improve the departure sequence at busy times of the day, by considering
the taxiing aircraft in addition to those already at the holding area. However, undertaking this re-introduces the issue of
taxi time uncertainty, the effect of which we explicitly measure in these experiments. Empirical results are presented for
experiments using real data from different times of the day, showing how the performance of the system varies depending upon
the volume of traffic and the accuracy of the provided taxi time estimations. We conclude that the development of a good taxi
time prediction system is key to maximising the benefits, although benefits can be observed even without this.

Mixed-Integer Programs (MIP's) involving logical implications mod- elled through big-M coe-cients, are notoriously among the hardest to solve. In this paper we propose and analyze computationally an au- tomatic problem reformulation of quite general applicability, aimed at removing the model dependency on the big-M coe-cients. Our solu- tion scheme deflnes a master Integer Linear Problem (ILP) with no continuous variables, which contains combinatorial information on the feasible integer variable combinations that can be \distilled" from the original MIP model. The master solutions are sent to a slave Linear Program (LP), which validates them and possibly returns combinato- rial inequalities to be added to the current master ILP. The inequal- ities are associated to minimal (or irreducible) infeasible subsystems of a certain linear system, and can be separated e-ciently in case the master solution is integer. The overall solution mechanism resembles closely the Benders' one, but the cuts we produce are purely com- binatorial and do not depend on the big-M values used in the MIP formulation. This produces an LP relaxation of the master problem which can be considerably tighter than the one associated with origi- nal MIP formulation. Computational results on two speciflc classes of hard-to-solve MIP's indicate the new method produces a reformulation which can be solved some orders of magnitude faster than the original MIP model.

The optimal allocation of indivisible resources is formalized as a
stochastic optimization problem involving discrete decision variables.
A general stochastic search procedure is proposed, which develops
the concept of the branch-and-bound method. The main idea is to process
large collections of possible solutions and to devote more attention
to the most promising groups. By gathering more information to reduce
the uncertainty and by narrowing the search area, the optimal solution
can be found with probability one. Special techniques for calculating
stochastic lower and upper bounds are discussed. The results are
illustrated by a computational experiment.

The optimal use of indivisible resources is often the central issue in the economy and management. One of the main difficulties is the discontinuous nature of the resulting resource allocation problems which may lead to the failure of competitive market allocation mechanisms (unless we agree to "divide" the indivisibles in some indirect way). The problem becomes even more acute when uncertainty of the outcomes of decisions is present.
In this paper we formalize the problem as a stochastic optimization problem involving discrete decision variables and uncertainties. By using some concrete examples, we illustrate how some problems of "dividing indivisibles" under uncertainty can be formalized in such terms. Next, we develop a general methodology to solve such problems based on the concept of the branch and bound method. The main idea of the approach is to process large collections of possible solutions and to devote more attention to the most promising groups. By gathering more information to reduce the uncertainty and by specializing the solution the optimal decision can be found.

In this paper a combinatorial optimization approach to aircraft sequencing problem is proposed. In particular the single runway case, with the hypotesis that airplanes wait to land at different times, is considered.
It is shown that the problem of maximizing the runway utilization can be modeled as a n job-one machine scheduling problem with non zero ready times, sequence dependent processing times, and with the objective of minimizing the maximum completion time.
A solution algorithm is outlined and tested by various examples and the computational results are discussed.
Implementation issues are also considered and suggestions on how improve the algorithm performances are made.

Aircraft arrive in a random fashion into a terminal area seeking to land at a given runway. The aircraft are differentiated by their landing velocities. All aircraft are required to maintain a prespecified minimum horizontal separation distance and also fly on a common final approach. As a consequence, the minimum interarrival time separation is interactive, i.e., a function of the landing velocities of the preceding and following aircraft as well as the separation minimum and final approach length. The controller's decision-making problem in sequencing the aircraft, termed dynamic scheduling, is formulated in this dynamic environment. It is observed that the first-come, first-serve discipline is inefficient and the system properties employing optimality objectives of maximum throughput and minimum delay are investigated. The solutions must be updated with each new arrival and, as a result, the solutions employing these optimality objectives are shown to have undesirable properties, including 1) a priority structure with the potential for indefinite delay; 2) non-implementable updating assignments; 3) computationally intractable solutions in real time. As a consequence of this analysis, a decision methodology termed Constrained Position Shifting (CPS) is proposed to eliminate these undesirable properties. CPS prohibits an aircraft from being shifted more than a given number of positions from its first-come, first-serve position. The CPS methodology is then shown via simulation to be practical, efficient and extremely flexible, with the following properties: 1. increases the runway throughput rate; 2. treats individual aircraft equitably; 3. treats aircraft velocity classes equitably; 4. particularly successful during peak periods; 5. well within the capabilities of today's computers. The simulation is designed to compare identical arrival streams under various strategies. The simulation-aided analysis is then extended to include "heavy" jets (with aircraft dependent separation minima) and also mixed operations (arrivals and departures). Even greater improvements in terminal area levels of service are demonstrated for these extensions.

A stochastic runway planning model has been developed for scheduling of airport runway operations in the presence of uncertainty, where stochastic attributes include pushback delay, time spent on taxiway, and deviation from estimated arrival time. The runway planning problem is modeled as a process in two stages, where the first stage uses a two-stage stochastic program to find an aircraft weight-class sequence that maximizes throughput while simultaneously achieving a desirable sequence for the second planning stage without having exact information on the stochastic parameters. In the second planning stage, individual aircraft are assigned to the sequence after exact information becomes available. The computational study shows that under certain assumptions, if the schedule is dense enough, there is a potential benefit of using the stochastic runway planner over a first-come, first-served planning policy or a deterministic runway planner.

Models and algorithms for real-time control of the terminal area are proposed. We consider two cases: in the first one (static) we assume that there is a set of aircraft to be sequenced for which we know in advance their entry time in the terminal area; in the second one (dynamic), the entry times of future aircraft are unknown and the sequence of aircraft is recomputed whenever a new aircraft approaches the terminal area. For the static case, we model the sequencing problem as a cumulative traveling salesman problem with ready times and propose two lower bounds for testing heuristic solutions. For the dynamic case, where only a limited knowledge of the arrivals is assumed, we add to the basic model a set of constraints which allow the controller to maintain given patterns of the landing sequences previously generated. For both cases, heuristic algorithms are proposed and computational results are discussed.

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. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

A stochastic branch-and-bound technique for the solution of stochastic single-machine-tardiness problems with job weights is presented. The technique relies on partitioning the solution space and estimating lower and upper bounds by sampling. For the lower bound estimation, two different types of sampling (“within” and “without” the minimization) are combined. Convergence to the optimal solution (with probability one) can be demonstrated. The approach is generalizable to other discrete stochastic optimization problems. In computational experiments with the single-machine-tardiness problem, the technique worked well for problem instances with a relatively small number of jobs; due to the enormous complexity of the problem, only approximate solutions can be expected for a larger number of jobs. Furthermore, a general precedence rule for the single-machine scheduling of jobs with uncertain processing times has been derived, essentially saying that “safe” jobs are to be scheduled before “unsafe” jobs.

We consider parallel, identical machine scheduling problems, where the jobs are subject to precedence constraints and release dates, and where the processing times of jobs are governed by independent probability distributions. Our objective is to minimize the expected value of the total weighted completion time. Building upon a linear programming relaxation by Mohring, Schulz, and Uetz (J. ACM, 46 (1999), pp. 924-942) and a delayed list scheduling algorithm by Chekuri et al. (SIAM J. Comput., 31 (2001), pp. 146-166), we derive the first constant-factor approximation algorithms for this model.

To understand how greatly new computer-based Decision Support Systems can benefit air traffic control, we study air traffic delays for landing aircraft at Boston. First, we develop an empirical model for present day Landing Time Intervals (LTIs) between aircraft in terms of two factors that significantly affect them: the landing runway configuration and the weight-class categories of the aircraft. Next, we develop three increasingly rich models of Boston's terminal airspace and apply, on airflow data, sequencing algorithms meant to expedite the landing of incoming aircraft. Comparing sequences suggested by the algorithms to those now used by controllers, we estimate that better sequencing can reduce delays by 30% in some instances. However, such improvements must be balanced against the effects such algorithms would have on workloads and other aspects of the air traffic control environment.

We find the most efficient (airport) runway utilization by using a methodology which we call Constrained Position Shifting (CPS). We examine this methodology from the perspectives of both pilots and air traffic controllers by simulation. The results indicate that significant and equitable improvements in system performance are achieved, especially during peak periods.

This paper presents results from a doctoral dissertation (reference
12), on the problem of
scheduling with Maximum Position Shift (MPS) constraints.
The problem typically arises in a
queueing system, when the service rate depends on the sequence in which
customers are
handled by the server. Such a queueing system is the airport runway system,
where it has been
shown (references 3, 10, 12) that rearranging the sequence of landings
and takeoffs affects the
runway capacity – that is, the rate of runway operations. An optimal
Dynamic Programming
(DP) scheduling algorithm is developed that takes as
input the set of currently known flights,
their desired time of operation, basis of the First Come First
Served (FCFS) sequence, and a
matrix of Air Traffic Control (ATC) minimum time separations,
in order to produce an optimal
schedule defined as runway and threshold time assignments maximizing runway
capacity.

We study a single-machine stochastic scheduling problem with n jobs, in which each job has a random processing time and a general stochastic cost function which may include a random due date and weight. The processing times are exponentially distributed, whereas the stochastic cost functions and the due dates may follow any distributions. The objective is to minimize the expected sum of the cost functions. We prove that a sequence in an order based on the product of the rate of processing time with the expected cost function is optimal, and under certain conditions, a sequence with the weighted shortest expected processing time first (WSEPT) structure is optimal. We show that this generalizes previous known results to more general situations. Examples of applications to practical problems are also discussed.

An algorithm for optimal arrival flight sequencing and spacing in a near-terminal area is proposed. The optimization problem and algorithm proposed in this paper are developed for a decision-support tool for air-traffic control, which uses discrete delay times as optimization variables. The algorithm is applicable to various scenarios with situational and operational constraints such as maximum position shift (MPS) constraints or different sets of discrete delay times, depending on aircraft types or approaching routes. The proposed algorithm is based on a branch-and-bound algorithm with linear programming (LP) and Lagrangian dual decomposition. We formulate the sequencing and scheduling problem as LP with linear matrix inequalities (LMIs), which allows computing the lower bound of the cost for the best first search in the branch-and-bound algorithm and propose Lagrangian dual decomposition for computational efficiency. The proposed algorithm is analyzed and validated through illustrative air-traffic scenarios with various operational constraints, and the simulation results show that the computation time can be significantly reduced using the proposed Lagrangian dual-decomposition method.

A methodology is proposed for sequencing and scheduling of aircraft in high density terminal areas. Termed Constrained Position Shifting (CPS), this methodology is examined and its effectiveness tested. Potential capacity improvements are noted over the First-Come, First-Served, Runway (FCFS-RW) strategy, especially during peak periods.

Airport runway optimization is an ongoing challenge for air traffic controllers. Since demand for air-transportation is predicted
to increase, there is a need to realize additional take-off and landing slots through better runway scheduling. In this paper,
we review the techniques and tools of operational research and management science that are used for scheduling aircraft landings
and take-offs. The main solution techniques include dynamic programming, branch and bound, heuristics and meta-heuristics.

The efficient operation of airports, and runways in particular, is critical to the throughput of the air transportation system as a whole. Scheduling arrivals and departures at runways is a complex problem that needs to address diverse and often competing considerations of efficiency, safety, and equity among airlines. One approach to runway scheduling that arises from operational and fairness considerations is that of constrained position shifting (CPS), which requires that an aircraft's position in the optimized sequence not deviate significantly from its position in the first-come-first-served sequence. This paper presents a class of scalable dynamic programming algorithms for runway scheduling under constrained position shifting and other system constraints. The results from a prototype implementation, which is fast enough to be used in real time, are also presented.

The problem of scheduling aircraft landings on one or more runways is an interesting problem that is similar to a machine job scheduling problem with sequence-dependent processing times and with earliness and tardiness penalties. The aim is to optimally land a set of planes on one or several runways in such a way that separation criteria between all pairs of planes (not just successive ones) are satisfied. Each plane has an allowable time window as well as a target time. There are costs associated with landing either earlier or later than this target landing time. In this paper, we present a specialized simplex algorithm which evaluates the landing times very rapidly, based on some partial ordering information. This method is then used in a problem space search heuristic as well as a branch-and-bound method for both single- and multiple-runway problems. The effectiveness of our algorithms is tested using some standard test problems from the literature. © 1999 John Wiley & Sons, Inc. Networks 34: 229–241, 1999

We present an algorithm for solving stochastic integer programming
problems with recourse, based on a dual decomposition scheme and
Lagrangian relaxation. The approach can be applied to multi-stage
problems with mixed-integer variables in each time stage. Numerical
experience is presented for some two-stage test problems.

Although various airport landing sequencing algorithms have been considered in the literature, little work has been done in comparing their effects on Air Traffic Control, especially against first-come first-served (FCFS) runway sequences, the method most widely used in practice. This paper compares a number of such algorithms using a discrete-event simulation model of an airport with a single landing runway. Statistical methods are used to test for effects of sequencing algorithm, delay-sharing strategy, arrival rate and wake-vortex mix. Little benefit to delay, or stability of sequencing advice, is found from advanced sequencing when small changes are made to inputs calibrated to a specific airspace. Advanced sequencing improves landing rate, compared with FCFS sequencing, only when aircraft arrival rate is greater than maximum runway landing rate, and wake-vortex mix is sufficiently varied. Constrained position shifting constraints limit these improvements and it is shown that deterministic optimal techniques may actually be sub-optimal in a dynamic environment. Our main conclusion is that FCFS is a robust method under many conditions.

This paper studies the static single machine scheduling problem with earliness and tardiness costs where job processing times are random variables and due dates are distinct and deterministic. The objective is to identify an optimal sequence which minimizes the total expeted earliness plus tardiness cost. A case where processing times are normally distributed is fully explored. We demonstrate that variations in processing times increase cost and affect sequencing decisions. Three heuristics for finding an optimal sequence are proposed. The illustrative example and computational results indicate that optimal sequences and their expected costs are significantly different from those provided by the classical deterministic single machine models. Furthermore, our computational experiments show that two of the proposed heuristics perform well in identifying optimal sequences.

This paper is concerned with the problems in scheduling a set of jobs associated with random due dates on a single machine so as to minimize the expected maximum lateness in stochastic environment. This is a difficult problem and few efforts have been reported on its solution in the literature. In this paper, we first derive a deterministic equivalent to the expected maximum lateness and then propose a dynamic programming algorithm to obtain the optimal solutions. The procedures to compute optimal solutions are initially developed in the case of deterministic processing times, and then extended to stochastic processing times following arbitrary probability distributions. Moreover, several heuristic rules are suggested to compute near-optimal solutions, which are shown to be highly efficient and accurate by computer-based experiments.

A novel scheduling algorithm has been designed and coded to
optimize arrival aircraft sequences and schedules. This algorithm,
called the implicit enumeration (IE) scheduling algorithm, has been
adopted as the foundation of the Traffic Management Advisor which is
part of the Center/Terminal Radar Approach Control (TRACON) Automation
System (CTAS). Because of the dynamic nature of air traffic control, the
IE scheduling algorithm has been developed to operate in a dynamic
feedback environment. The algorithm structure which controls the
scheduling feedback also provides the platform for other advances. The
criteria to be optimized can be specified flexibly, and can be varied
on-line. Another feature of the algorithm applies to the situation found
at many high-density airports, where multiple runways are used for
arrivals simultaneously. The approach taken in the algorithm allows the
planning process to be expanded to include runway assignment. Initial
results from using the IE algorithm for runway assignment indicate that
significant performance enhancements are possible when both runway and
sequence assignments are considered in the scheduling process. This
algorithm was first used in early 1992 at the Denver Air Route Traffic
Control Center for the first stages of the field evaluation of CTAS by
the FAA

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