Fairness in Slot Allocation

The recent interpretations of fairness in slot allocation of flights are considered as the word equity and upon these interpretations for fairness, aviation agencies as airspace administrators along with stakeholders have been applying ground delay problem procedure with ration by schedule and compression algorithms as fair distribution of slots among them in reduced capacity airports. The drawback of these approaches is that the slots to be allocated to flights are all of the equal size or duration since the flights to be assigned to slots can not be differentiated. In fact, the absence of a scientific framework of fairness in air traffic management has led to the different contradictory interpretations for it. As proposed in this study, fairness is the minimum deviation from the planned outcome in terms of time, quantity and quality under the optimum share management rule for each stakeholder. To achieve fairness in slot allocation of the airport under reduced and normal capacity, a new allocation rule of ration by fairness is proposed in which the elements of time, quantity and quality are proposed to be the original time of departure or arrival, slot size or duration, and airspace safety and preflight checklist, respectively

Multi-Objective, Multi-Stakeholder Airport Slot Scheduling Considering Expected Delays

We present a multi-objective, multi-stakeholder decision making framework for airport slot scheduling decisions. The framework generates the complete set of non-dominated schedules for any triplet of linear slot scheduling objectives. To deal with the decision-making complexity arising from the large number of efficient schedules, we introduce a subtractive clustering algorithm to select a set of representative high-quality schedules. We estimate the expected delays associated with each representative schedule and we incorporate stakeholders’ preferences to select the most preferable airport schedule using schedule displacement and operational delay metrics

Applications of stochastic modeling in air traffic management:Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management

Modelling and solving the airport slot-scheduling problem with multi-objective, multi-level considerations

In overly congested airports requests for landing and take-off slots are allocated according to the IATA World Scheduling Guidelines (WSG). A central concept of these guidelines is the prioritization of the satisfaction of the requested slots according to a hierarchy that recognizes historic usage rights of slots. A number of criteria have been proposed in the literature to optimize airport slot allocation decisions. Multi-objective programming models have been proposed to investigate the trade-offs of the slot allocation objectives for the same level of the slot hierarchy. However, the literature currently lacks models that can study in a systematic way the trade-offs among the scheduling objectives across all levels of the hierarchy and the airport schedule as a whole. To close the existing literature gap, we are proposing a new tri-objective slot allocation model (TOSAM) that considers total schedule displacement, maximum schedule displacement and demand-based fairness, and we introduce a multi-level, multi-objective algorithm to solve it. We are using real world slot request and airport capacity data to demonstrate the applicability of the proposed approach. Our computational results suggest that the systematic consideration of the interactions among the objectives of the different levels of the slot hierarchy, results to improved schedule-wide slot scheduling performance. In particular, we found that small sacrifices made for the attainment of the scheduling objectives of the upper echelons of the slot hierarchy, result in significant improvements of the schedule-wide objectives

A slot scheduling mechanism at congested airports which incorporates efficiency, fairness and airline preferences

Congestion is a problem at airports where capacity does not meet demand. At many such airports, airlines must request time slots for the purpose of landing or take off. Given the imbalance between demand and capacity, slot requests cannot always be scheduled as requested. The difference between the requested and allocated time slots is called displacement. Minimization of the total displacement is a key slot-scheduling objective and expresses the efficiency of the slot-scheduling process. Additionally, fairness has been proposed as a slot-scheduling criterion. Fairness relates to the allocation of the total schedule displacement among the various airlines. Single- and multiobjective models have been proposed for slot scheduling. However, currently the literature lacks models that incorporate the preferences of airlines regarding the allocation of displacement to their flights. This paper proposes a two-stage mechanism for the scheduling of slots at congested airports. The proposed mechanism considers efficiency and fairness objectives and incorporates the preferences of airlines in allocating the total displacement associated with the flights of each airline. The first stage of the mechanism constructs a reference schedule that is fair to the participating airlines. In the second stage, the airlines specify how the displacement allocated to them in the reference schedule should be distributed among their requests. The mechanism then adjusts the fair reference schedule to meet as many of these preferences as possible. The development and implementation of the proposed slot-scheduling mechanism is demonstrated using real data from a coordinated airport and simulated displacement preference data. The proposed slot-scheduling mechanism provides useful information to decision makers regarding the equity–efficiency trade-off and enhances the transparency and acceptability of the slot-scheduling outcome

Optimal network-wide adjustments of initial airport slot allocations with connectivity and fairness objectives

Due to serious demand-supply imbalances, many airports around the world are highly congested. Access to these highly congested (Level 3, coordinated) airports is controlled through the use of the IATA World Airport Slot allocation Guidelines (WASG). At an individual airport, slots requested by each airline are allocated at the airport under consideration independently without taking into account the interactions between slots allocated at different airports. However, in order for the air-transport network to operate seamlessly, ensuring network-wide connectivity of flights, and the interdependencies existing between the slots allocated at individual airports need to be considered. Several models have been proposed in the literature to deal with the optimum allocation of slots at a single airport. However, the literature currently does not adequately address the network-wide slot allocation problem. In this paper, we are introducing a novel approach to address the network-wide slot allocation problem. Our approach considers as an input the individual airport schedules generated during the slot allocation process at individual airports and optimally adjusts them to ensure network-wide flight connectivity by taking into account the interdependencies existing between flights connecting pairs of airports. To this end, we propose bi-objective mathematical models, which consider schedule efficiency and inter-airline fairness objectives, and incorporate the importance that different airports have for the functioning of the air transport network, using the IATA connectivity indices and the betweenness centrality measures. We solve the proposed models using the ε − constraint method to investigate trade-offs between network-wide schedule efficiency and fairness, and we investigate the effect of these trade-offs on the airlines and the airports. Results from the application of the proposed models to a test network suggest that the consideration of the contribution of the airports to network connectivity affect the way that the total network-wide schedule displacement is distributed among the airports. Specifically, we found that the use of the IATA connectivity index tends to allocate less schedule displacement to airports with frequent flights to many destinations, while the use of the betweenness centrality measure allocates less schedule displacement to airports that are more critical in ensuring the connectivity of other airports in the network

Central authority controlled air traffic flow management: An optimization approach.

Despite various planning efforts, airspace capacity can sometimes be exceeded, typically due to disruptive events. Air traffic flow management (ATFM) is the process of managing flights in this situation. In this paper, we present an ATFM model that accounts for different rerouting options (path rerouting and diversion) and pre-existing en-route flights. The model proposes having a central authority to control all decisions, which is then compared with current practice. We also consider inter-flight and inter-airline fairness measures in the network. We use an exact approach to solve small-to-medium-sized instances, and we propose a modified fix-and-relax heuristic to solve large-sized instances. Allowing a central authority to control all decisions increases network efficiency compared to the case where the ATFM authority and airlines control decisions independently. Our experiments show that including different rerouting options in ATFM can help reduce delays by up to 8% and cancellations by up to 23%. Moreover, ground delay cost has much more impact on network decisions than air delay cost, and network decisions are insensitive to changes in diversion cost. Furthermore, the analysis of the trade-off between total network cost and overtaking cost shows that adding costs for overtaking can significantly improve fairness at only a small increase in total system cost. A balanced total cost per flight among airlines can be achieved at a small increase in the network cost (0.2 to 3.0%) when imposing airline fairness. In conclusion, the comprehensiveness of the model makes it useful for analyzing a wide range of alternatives for efficient ATF

Probabilistic bounds on the k−k-Traveling Salesman Problem and the Traveling Repairman Problem

The $k-$traveling salesman problem ($k$-TSP) seeks a tour of minimal length that visits a subset of $k\leq n$ points. The traveling repairman problem (TRP) seeks a complete tour with minimal latency. This paper provides constant-factor probabilistic approximations of both problems. We first show that the optimal length of the $k$-TSP path grows at a rate of $\Theta\left(k/n^{\frac{1}{2}\left(1+\frac{1}{k-1}\right)}\right)$. The proof provides a constant-factor approximation scheme, which solves a TSP in a high-concentration zone -- leveraging large deviations of local concentrations. Then, we show that the optimal TRP latency grows at a rate of $\Theta(n\sqrt n)$. This result extends the classical Beardwood-Halton-Hammersley theorem to the TRP. Again, the proof provides a constant-factor approximation scheme, which visits zones by decreasing order of probability density. We discuss practical implications of this result in the design of transportation and logistics systems. Finally, we propose dedicated notions of fairness -- randomized population-based fairness for the $k$-TSP and geographical fairness for the TRP -- and give algorithms to balance efficiency and fairness

Multi-objective, multi-level, multi-stakeholder considerations for airport slot allocation

Airport slot scheduling has attracted the attention of researchers as a capacity management tool at congested airports. In an attempt to better grasp the demands of the problem, recent research work has employed multi-objective optimisation (MOO) approaches. However, the multiple stakeholders (e.g. airlines, coordinators, aviation and local authorities), their numerous or even conflicting objectives and the complexity of the decision-process (rules and slot priorities), have rendered the holistic modelling of the slot allocation problem a demanding and yet incomplete task. Through a rigorous review of the policy rules and the identification of the modelling gaps in the ΜΟΟ airport slot allocation literature, this study aims to contribute to the field by proposing novel modelling considerations and solution approaches which accommodate additional characteristics of the real-world decision context. In detail, by building on previous research efforts, we propose a tri-objective slot allocation model (TOSAM), which jointly considers schedule delays, maximum displacement and demand-based fairness. We further proved that multi-level, game-theoretic-based considerations are suitable to capture the interactions among the different slot priorities, leading to enhanced airport slot schedules. To address the incurring complexity, we introduced the notion of inter-level tolerance and solved the TOSAM with systematic multi-level interactions for a medium sized airport. Our computational results suggest that by tolerating small objective function sacrifices at the upper decision levels, the resulting Pareto frontiers are of greater cardinality and quality in comparison to existing solution methods. Finally, we propose and illustrate two alternative bi-stage solution methods that exemplify the potential synergies between the MOO and multi-attribute decision-making literature

Modelling and Solving the Single-Airport Slot Allocation Problem

Currently, there are about 200 overly congested airports where airport capacity does not suffice to accommodate airline demand. These airports play a critical role in the global air transport system since they concern 40% of global passenger demand and act as a bottleneck for the entire air transport system. This imbalance between airport capacity and airline demand leads to excessive delays, as well as multi-billion economic, and huge environmental and societal costs. Concurrently, the implementation of airport capacity expansion projects requires time, space and is subject to significant resistance from local communities. As a short to medium-term response, Airport Slot Allocation (ASA) has been used as the main demand management mechanism. The main goal of this thesis is to improve ASA decision-making through the proposition of models and algorithms that provide enhanced ASA decision support. In doing so, this thesis is organised into three distinct chapters that shed light on the following questions (I–V), which remain untapped by the existing literature. In parentheses, we identify the chapters of this thesis that relate to each research question. I. How to improve the modelling of airline demand flexibility and the utility that each airline assigns to each available airport slot? (Chapters 2 and 4) II. How can one model the dynamic and endogenous adaptation of the airport’s landside and airside infrastructure to the characteristics of airline demand? (Chapter 2) III. How to consider operational delays in strategic ASA decision-making? (Chapter 3) IV. How to involve the pertinent stakeholders into the ASA decision-making process to select a commonly agreed schedule; and how can one reduce the inherent decision-complexity without compromising the quality and diversity of the schedules presented to the decision-makers? (Chapter 3) V. Given that the ASA process involves airlines (submitting requests for slots) and coordinators (assigning slots to requests based on a set of rules and priorities), how can one jointly consider the interactions between these two sides to improve ASA decision-making? (Chapter 4) With regards to research questions (I) and (II), the thesis proposes a Mixed Integer Programming (MIP) model that considers airlines’ timing flexibility (research question I) and constraints that enable the dynamic and endogenous allocation of the airport’s resources (research question II). The proposed modelling variant addresses several additional problem characteristics and policy rules, and considers multiple efficiency objectives, while integrating all constraints that may affect airport slot scheduling decisions, including the asynchronous use of the different airport resources (runway, aprons, passenger terminal) and the endogenous consideration of the capabilities of the airport’s infrastructure to adapt to the airline demand’s characteristics and the aircraft/flight type associated with each request. The proposed model is integrated into a two-stage solution approach that considers all primary and several secondary policy rules of ASA. New combinatorial results and valid tightening inequalities that facilitate the solution of the problem are proposed and implemented. An extension of the above MIP model that considers the trade-offs among schedule displacement, maximum displacement, and the number of displaced requests, is integrated into a multi-objective solution framework. The proposed framework holistically considers the preferences of all ASA stakeholder groups (research question IV) concerning multiple performance metrics and models the operational delays associated with each airport schedule (research question III). The delays of each schedule/solution are macroscopically estimated, and a subtractive clustering algorithm and a parameter tuning routine reduce the inherent decision complexity by pruning non-dominated solutions without compromising the representativeness of the alternatives offered to the decision-makers (research question IV). Following the determination of the representative set, the expected delay estimates of each schedule are further refined by considering the whole airfield’s operations, the landside, and the airside infrastructure. The representative schedules are ranked based on the preferences of all ASA stakeholder groups concerning each schedule’s displacement-related and operational-delay performance. Finally, in considering the interactions between airlines’ timing flexibility and utility, and the policy-based priorities assigned by the coordinator to each request (research question V), the thesis models the ASA problem as a two-sided matching game and provides guarantees on the stability of the proposed schedules. A Stable Airport Slot Allocation Model (SASAM) capitalises on the flexibility considerations introduced for addressing research question (I) through the exploitation of data submitted by the airlines during the ASA process and provides functions that proxy each request’s value considering both the airlines’ timing flexibility for each submitted request and the requests’ prioritisation by the coordinators when considering the policy rules defining the ASA process. The thesis argues on the compliance of the proposed functions with the primary regulatory requirements of the ASA process and demonstrates their applicability for different types of slot requests. SASAM guarantees stability through sets of inequalities that prune allocations blocking the formation of stable schedules. A multi-objective Deferred-Acceptance (DA) algorithm guaranteeing the stability of each generated schedule is developed. The algorithm can generate all stable non-dominated points by considering the trade-off between the spilled airline and passenger demand and maximum displacement. The work conducted in this thesis addresses several problem characteristics and sheds light on their implications for ASA decision-making, hence having the potential to improve ASA decision-making. Our findings suggest that the consideration of airlines’ timing flexibility (research question I) results in improved capacity utilisation and scheduling efficiency. The endogenous consideration of the ability of the airport’s infrastructure to adapt to the characteristics of airline demand (research question II) enables a more efficient representation of airport declared capacity that results in the scheduling of additional requests. The concurrent consideration of airlines’ timing flexibility and the endogenous adaptation of airport resources to airline demand achieves an improved alignment between the airport infrastructure and the characteristics of airline demand, ergo proposing schedules of improved efficiency. The modelling and evaluation of the peak operational delays associated with the different airport schedules (research question III) provides allows the study of the implications of strategic ASA decision-making for operations and quantifies the impact of the airport’s declared capacity on each schedule’s operational performance. In considering the preferences of the relevant ASA stakeholders (airlines, coordinators, airport, and air traffic authorities) concerning multiple operational and strategic ASA efficiency metrics (research question IV) the thesis assesses the impact of alternative preference considerations and indicates a commonly preferred schedule that balances the stakeholders’ preferences. The proposition of representative subsets of alternative schedules reduces decision-complexity without significantly compromising the quality of the alternatives offered to the decision-making process (research question IV). The modelling of the ASA as a two-sided matching game (research question V), results in stable schedules consisting of request-to-slot assignments that provide no incentive to airlines and coordinators to reject or alter the proposed timings. Furthermore, the proposition of stable schedules results in more intensive use of airport capacity, while simultaneously improving scheduling efficiency. The models and algorithms developed as part of this thesis are tested using airline requests and airport capacity data from coordinated airports. Computational results that are relevant to the context of the considered airport instances provide evidence on the potential improvements for the current ASA process and facilitate data-driven policy and decision-making. In particular, with regards to the alignment of airline demand with the capabilities of the airport’s infrastructure (questions I and II), computational results report improved slot allocation efficiency and airport capacity utilisation, which for the considered airport instance translate to improvements ranging between 5-24% for various schedule performance metrics. In reducing the difficulty associated with the assessment of multiple ASA solutions by the stakeholders (question IV), instance-specific results suggest reductions to the number of alternative schedules by 87%, while maintaining the quality of the solutions presented to the stakeholders above 70% (expressed in relation to the initially considered set of schedules). Meanwhile, computational results suggest that the concurrent consideration of ASA stakeholders’ preferences (research question IV) with regards to both operational (research question III) and strategic performance metrics leads to alternative airport slot scheduling solutions that inform on the trade-offs between the schedules’ operational and strategic performance and the stakeholders’ preferences. Concerning research question (V), the application of SASAM and the DA algorithm suggest improvements to the number of unaccommodated flights and passengers (13 and 40% improvements) at the expense of requests concerning fewer passengers and days of operations (increasing the number of rejected requests by 1.2% in relation to the total number of submitted requests). The research conducted in this thesis aids in the identification of limitations that should be addressed by future studies to further improve ASA decision-making. First, the thesis focuses on exact solution approaches that consider the landside and airside infrastructure of the airport and generate multiple schedules. The proposition of pre-processing techniques that identify the bottleneck of the airport’s capacity, i.e., landside and/or airside, can be used to reduce the size of the proposed formulations and improve the required computational times. Meanwhile, the development of multi-objective heuristic algorithms that consider several problem characteristics and generate multiple efficient schedules in reasonable computational times, could extend the capabilities of the models propositioned in this thesis and provide decision support for some of the world’s most congested airports. Furthermore, the thesis models and evaluates the operational implications of strategic airport slot scheduling decisions. The explicit consideration of operational delays as an objective in ASA optimisation models and algorithms is an issue that merits investigation since it may further improve the operational performance of the generated schedules. In accordance with current practice, the models proposed in this work have considered deterministic capacity parameters. Perhaps, future research could propose formulations that consider stochastic representations of airport declared capacity and improve strategic ASA decision-making through the anticipation of operational uncertainty and weather-induced capacity reductions. Finally, in modelling airlines’ utility for each submitted request and available time slot the thesis proposes time-dependent functions that utilise available data to approximate airlines’ scheduling preferences. Future studies wishing to improve the accuracy of the proposed functions could utilise commercial data sources that provide route-specific information; or in cases that such data is unavailable, employ data mining and machine learning methodologies to extract airlines’ time-dependent utility and preferences