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

An Optimisation Framework for Airline Fleet Maintenance Scheduling with Tail Assignment Considerations

Fierce competition between airlines has led to the need of minimising the operating costs while also ensuring quality of service. Given the large proportion of operating costs dedicated to aircraft maintenance, cooperation between airlines and their respective maintenance provider is paramount. In this research, we propose a framework to develop commercially viable and maintenance feasible flight and maintenance schedules. Such framework involves two multi-objective mixed integer linear programming (MMILP) formulations and an iterative algorithm. The first formulation, the airline fleet maintenance scheduling (AMS) with violations, minimises the number of maintenance regulation violations and the number of not airworthy aircraft; subject to limited workshop resources and current maintenance regulations on individual aircraft flying hours. The second formulation, the AMS with tail assignment (TA) allows aircraft to be assigned to different flights. In this case, subject to similar constraints as the first formulation, six lexicographically ordered objective functions are minimised. Namely, the number of violations, maximum resource level, number of tail reassignments, number of maintenance interventions, overall resource usage, and the amount of maintenance required by each aircraft at the end of the planning horizon. The iterative algorithm ensures fast computational times while providing good quality solutions. Additionally, by tracking aircraft and using precise flying hours between maintenance opportunities, we ensure that the aircraft are airworthy at all times. Computational tests on real flight schedules over a 30-day planning horizon show that even with multiple airlines and workshops (16000 flights, 529 aircraft, 8 maintenance workshops) our solution approach can construct near-optimal maintenance schedules within minutes

Considering spatial and temporal flexibility in optimizing one-way electric carsharing systems

Carsharing is a shared-use vehicle model that allows users to rent cars for short periods of times. There are different types of systems according to their operational properties. In round-trip carsharing systems users are expected to return vehicles to their pickup locations. One-way systems relax this restriction and allows users to return cars to different drop-off locations. In station-based systems, there are designated parking locations to which vehicles should be returned. Free-floating systems relax this restriction and allow users to park vehicles to any legal parking locations within a designated area. In this research we are dealing with operational planning decisions in station-based one-way electric carsharing systems with dynamic relocations. Different than the previous work in literature, we introduce spatial and temporal flexibility to the system by considering multiple pick-up and drop-off times and locations at different prices to increase total profit of the system

Modelling and solving the combined inventory routing problem with risk consideration

This work proposes a multi-objective extension of a real-world inventory routing problem (IRP), a generalisation of the classical vehicle routing problem (VRP) with vendor managed inventory (VMI) replenishment. While many mathematical formulations and solution models already exist, this study incorporates business related and risk considerations that makes it unique. It is known that a significant volume of hazardous materials travels every day. Consideration of risks arising from the transportation of hazardous materials as a criterion for selecting distribution routes could potentially reduce the likelihood of accidents and/or the expected consequences of accident

Incorporating declared capacity uncertainty in optimizing airport slot allocation

Slot allocation is the mechanism used to allocate capacity at congested airports. A number of models have been introduced in the literature aiming to produce airport schedules that optimize the allocation of slot requests to the available airport capacity. A critical parameter affecting the outcome of the slot allocation process is the airport’s declared capacity. Existing airport slot allocation models treat declared capacity as an exogenously defined deterministic parameter. In this presentation we propose a new robust optimization formulation based on the concept of stability radius. The proposed formulation considers endogenously the airport’s declared capacity and expresses it as a function of its throughput. We present results from the application of the proposed approach to a congested airport and we discuss the trade-off between the declared capacity of the airport and the efficiency of the slot allocation process

Investigating the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems

One-way electric carsharing systems provide an environmentally friendly option for facilitating urban mobility needs. However, the management of one-way electric carsharing systems presents operational challenges stemming from the need to relocate cars in order to strike an optimum balance between demand and supply. As a result, the cost associated with vehicle relocation operations represents a significant proportion of the total operating cost. In the context of electric carsharing systems, the problem of vehicle relocation is further exacerbated by the car battery charging requirements. The introduction of temporal and spatial flexibility regarding the pick-up and drop-off of vehicles provides the means of improving the efficiency of one-way electric carsharing systems. However, the literature currently lacks models that can be used to investigate the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems. In this paper, we are introducing an integrated modeling and solution framework for investigating the effect of temporal and/or spatial flexibility, and different options for processing trip requests to the profitability and utilization of one-way electric carsharing systems. The application of the proposed framework to a realistic size system suggests that spatial flexibility has a stronger effect on the system performance than temporal flexibility. Furthermore, both spatial and temporal flexibility can increase the profitability of the system by serving more customers with fewer vehicle relocation needs

Incorporating the value of slots in airport slot scheduling decisions

Airport slot allocation is the dominant mechanism for managing capacity at congested airports outside the United States. Current practice is facilitated via expert systems software that apply a complex decision process defined by various criteria, rules and priorities. It is acknowledged that mathematical programming may result in more efficient airport slot schedules. Yet, the incorporation of all the regulations and characteristics of the decision process results in complex mathematical formulations and increased computational times. At the same time, existing models assume that a “slot is a slot” without taking into account the differences in the characteristics and significance of each slot. In this work, through a multi-criteria – multi-stakeholder approach, we introduce a slot valuation index (SVI) that considers the attributes of each airport slot while simultaneously incorporating the preferences of all participating groups of stakeholders. We move beyond the proposal of the SVI by devising a two-stage solution approach that employs the SVI as a relative importance weight in the objective functions of optimisation models. Our approach is able to address additional policy requirements, criteria and slot characteristics while preserving computational tractability

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

An optimization framework for the development of efficient one-way car-sharing systems

Environmental, energy, and societal considerations have given rise to the concept of shared-vehicle mobility systems. This concept postulates that the use of a fleet of vehicles made available on demand to the general public on a rental basis, can increase the mobility of certain population categories. In addition to mobility enhancement, shared-vehicle mobility systems have the potential to contribute to the sustainability of the transportation system through the decrease of environmental impacts, energy and space requirements (Duncan, 2011). As a consequence of the promises that shared-vehicle mobility systems hold, numerous such systems have been introduced in many cities around the world (Barth et al., 2006). However, most of the real-world applications of the car-sharing systems works in two ways, i.e. the vehicle should be returned to where it is rented from. Although there are some examples of one-way car-sharing systems in practice, they are not preferred by the operators because of their operational difficulties (e.g. relocations of vehicles). In this research we aim to propose a generic model for supporting the strategic (station location and size) and tactical (fleet size) decisions of a general one-way car-sharing system, with a direct application in a case study in Nice, France. For this purpose, a mathematical model is formulated and sensitivity analysis is conducted for different parameters. As a future work, we plan to work on the operational problem which considers requests on-line and updates vehicle rosters accordingly