Flight Legs Research Articles

A two-level optimization approach for robust aircraft routing and retiming

We investigate the Robust Aircraft Routing and Retiming Problem that is defined as follows. Given a set of flight legs to be served by a set of aircraft fleets, together with a tentative schedule, the problem requires determining a route assignment for each aircraft and the departure time of each flight leg so as to cover each flight by exactly one aircraft while satisfying operational constraints. The objective is to derive robust solutions that are less vulnerable to unpredictable disruptions caused by late-arriving aircraft. Ultimately, the goal being to enhance the airline on-time performance which is considered as a key performance measure since it greatly impinge on the airline profitability. In this paper, robustness is achieved through inserting time buffers in front of selected flight departure times. Toward this end, we propose a novel two-level solution strategy that embeds a simulation-optimization procedure within an evolutionary algorithm. At the first level, two mixed-integer quadratic programming models are iteratively solved for generating feasible trial solutions whose robustness is assessed by invoking a simulation procedure together with a Particle Swarm Optimization (PSO) procedure for guiding the search process. At the second level, an evolutionary algorithm is used for iteratively improving the solution that is generated at the first level. We present the results of extensive computational experiments that were carried out on a set of real data, with up to 1278 flights, and that demonstrate the benefits of the two-level approach.

Robust Aircraft Routing

We propose a robust optimization approach to minimize total propagated delay in the aircraft routing problem. Instead of minimizing the expected total propagated delay by assuming that flight leg delays follow specific probability distributions, our model minimizes the maximal possible total propagated delay when flight leg delays lie in a prespecified uncertainty set. We develop exact and tractable solution approaches for our robust model. The major contribution of our model is that it allows us to explicitly model and handle correlation in flight leg delays (e.g., because of weather or various air traffic management initiatives) that existing approaches cannot efficiently incorporate. Using both historical delay data and simulated data, we evaluate the performance of our model and benchmark against the state-of-the-research stochastic approach. In most of the cases, we observe that our model outperforms the existing approach in lowering the mean, reducing volatility, and mitigating extreme values of total propagated delay. In the cases where a deficit in one of the three criteria exists, gains in the other two criteria usually offset this disadvantage. These results suggest that robust optimization approaches can provide promising results for the aircraft routing problem. The online appendix is available at https://doi.org/10.1287/trsc.2015.0657 .

Stratospheric Gravity Wave Fluxes and Scales during DEEPWAVE

Abstract During the Deep Propagating Gravity Wave Experiment (DEEPWAVE) project in June and July 2014, the Gulfstream V research aircraft flew 97 legs over the Southern Alps of New Zealand and 150 legs over the Tasman Sea and Southern Ocean, mostly in the low stratosphere at 12.1-km altitude. Improved instrument calibration, redundant sensors, longer flight legs, energy flux estimation, and scale analysis revealed several new gravity wave properties. Over the sea, flight-level wave fluxes mostly fell below the detection threshold. Over terrain, disturbances had characteristic mountain wave attributes of positive vertical energy flux (EFz), negative zonal momentum flux, and upwind horizontal energy flux. In some cases, the fluxes changed rapidly within an 8-h flight, even though environmental conditions were nearly unchanged. The largest observed zonal momentum and vertical energy fluxes were MFx = −550 mPa and EFz = 22 W m−2, respectively. A wide variety of disturbance scales were found at flight level over New Zealand. The vertical wind variance at flight level was dominated by short “fluxless” waves with wavelengths in the 6–15-km range. Even shorter scales, down to 500 m, were found in wave breaking regions. The wavelength of the flux-carrying mountain waves was much longer—mostly between 60 and 150 km. In the strong cases, however, with EFz > 4 W m−2, the dominant flux wavelength decreased (i.e., “downshifted”) to an intermediate wavelength between 20 and 60 km. A potential explanation for the rapid flux changes and the scale “downshifting” is that low-level flow can shift between “terrain following” and “envelope following” associated with trapped air in steep New Zealand valleys.

THE INTEGRATED AIRCRAFT ROUTING AND CREW PAIRING PROBLEM: ILP BASED FORMULATIONS

Minimization of cost is very important in airline as great profit is an important objective for any airline system. One way to minimize the costs in airline is by developing an integrated planning process. Airline planning consists of many difficult operational decision problems including aircraft routing and crew pairing problems. These two sub-problems, though interrelated in practice, are usually solved sequentially leading to suboptimal solutions. We propose an integrated aircraft routing and crew pairing problem model, one approach to generate the feasible aircraft routes and crew pairs, followed by three approaches to solve the integrated model. The integrated aircraft routing and crew scheduling problem is to determine a minimum cost aircraft routes and crew schedules while each flight leg is covered by one aircraft and one crew. The first approach is an integer programming solution method, the second formulation is developed in a way to lend itself to be used efficiently by Dantzig Wolfe decomposition whereas the third one is formulated as a Benders decomposition method. Encouraging results are obtained when tested on four types of aircraft based on local flights in Malaysia for one week flight cycle.

Optimization models in RM systems: Optimality versus revenue gains

Optimization models in airline revenue management (RM) systems have evolved from single flight leg to network revenue maximization to marginal revenue optimization for less restricted fare structures. This article reviews the most common optimization approaches that have been widely implemented in airline RM systems, with a focus on how the mismatch between model assumptions and reality can affect achievable revenue performance. Simulation findings from the Passenger Origin-Destination Simulator are used to illustrate how robustness and revenue gains, as opposed to theoretical optimality, have driven the widespread adoption of practical optimization models in RM systems.

A novel column generation strategy for large scale airline crew pairing problems

A crew pairing is a sequence of flight legs beginning and ending at the same crew domicile. Crew pairing planning is the primary cost-determining phase in airline crew scheduling. Optimizing crew pairings of an airline timetable is an extremely important process which helps to minimize operational crew costs and to maximize crew utilization.There are various restrictions imposed by regulations or company policies that must be considered and satisfied in crew pairing generation process. Keeping these restrictions and regulations in mind, the main goal of the optimization is the generation of low cost sets of valid crew pairings which cover all flights in airline's timetable.For this research study, already existing works related to crew pairing optimization are examined and a new column generation strategy, a pricing network design and a pairing elimination heuristic are developed as a contribution to the previous studies. In the proposed strategy, the main problem is modeled and solved as a set-covering problem and the pricing sub problem is modeled as a shortest-path problem which is efficiently solved over a duty-flight overnight connection graph by the combined usage of heuristic and exact algorithms. The proposed strategy has been tested with real world data obtained from Turkish Airlines and it is seen that it is capable of generating very competitive solutions compared to current practices in Turkish Airlines. It is also observed that there are various advantages of proposed solution approach such as sensitivity to penalty coefficients, generating less deadheads, very close solution times with a single threaded software and light weight hardware.

Aircraft Line Maintenance Planning Based on PHM Data and Resources Availability Using Large Neighborhood Search


 
 
 Maintenance planning has become a topic of great interest among researchers and industry practitioners in recent years, since it directly impacts the availability and the lifecycle cost of systems. In the aviation industry, maintenance planning becomes even more relevant due to the high availability expectations from aircraft operators and the high costs incurred when an aircraft becomes out of service. For this reason, some minor maintenance activities are carried out near the gate, between two consecutive flight legs. These activities are referred to as aircraft line maintenance. Planning line maintenance activities is critical because a problem in the execution of line maintenance may lead to flight delays and even flight cancellations. This paper presents a methodology for aircraft line maintenance planning including both the troubleshooting tasks and the repair activities. The proposed methodology uses a Large Neighborhood Search (LNS) algorithm in order to find the most appropriated time and location to perform line maintenance activities. The algorithm considers the precedence relation between a troubleshooting task and its respective repair activity, as well as the dispachability constraints included in the MEL (Minimum Equipment List). Resources availability such as spare parts, equipments and personnel are taken into account, as well as the risk of occurrence of an AOG (Aircraft on Ground) event, estimated from PHM (Prognostics and Health Monitoring) data. An AOG event is an event that leads to a flight cancelation. The optimization goal is to minimize the Expected Cost of Repair (ECR) considering both delay and AOG expenses. A numerical example is presented to illustrate the application of the proposed methodology.
 
 

Solving a large-scale crew pairing problem

Airline companies seek to solve the problem of determining an assignment of crews to a pre-determined flight schedule with minimum total cost, called the Crew Pairing Problem (CPP). Most of the existing studies focus on the CPP of North American airlines, which widely differs from that of most European airline companies in terms of the objective function, the flight structure, and the planning horizon. In this study, we develop an optimization-driven heuristic algorithm that can efficiently handle large-scale instances of the CPP that must be solved on a monthly basis. We perform computational experiments using flight schedules of an European airline company to test the performance of the solution method. Our computational results demonstrate that our algorithm is able to provide high-quality solutions to monthly instances with up to 27 000 flight legs.

Aircraft‐based observations of atmospheric boundary‐layer modification over Arctic leads

Leads are elongated channels in sea ice which play an important role for the heat and moisture exchange between the polar ocean and atmosphere. The aircraft campaign STABLE aimed to improve our current understanding of the formation of convective plumes over leads and their impact on the polar atmospheric boundary layer. It was carried out over the pack ice in the northern Fram Strait in March 2013. We present case studies of the boundary layer modification and turbulent fluxes over four wide leads, which differed strongly with respect to lead characteristics and environmental conditions. The observed near‐surface sensible heat fluxes ranged from 15 to 180 W m−2. The leads also induced an increase of the near‐surface temperature of up to 3.2 °C and a humidity increase of up to 0.2 g kg−1. In one of the cases, large entrainment fluxes exceeding 30% of the surface fluxes were observed. Vertical profiles of turbulent sensible heat and momentum fluxes were nonlinear downstream of the leads with a distinct flux maximum in the core of the convective plumes. In two cases, the plumes also strongly affected the wind field within the atmospheric boundary layer. Low‐level jets that existed in those cases in the region upstream of the leads disappeared in the plume region. Finally, it is shown that large errors can occur when flux measurements are derived from lead orthogonal flight legs only. Therefore, complex flight patterns, as presented in this study, are necessary to accurately determine the energy fluxes in the environment of leads.

Snow Growth and Transport Patterns in Orographic Storms as Estimated from Airborne Vertical-Plane Dual-Doppler Radar Data

Abstract Airborne vertical-plane dual-Doppler cloud radar data, collected on wind-parallel flight legs over a mountain in Wyoming during 16 winter storms, are used to analyze the growth, transport, and sedimentation of snow. In all storms the wind is rather strong, such that the flow is unblocked. The sampled clouds are mixed phase, shallow, and generally produce snowfall over the mountain only. The 2D scatterers’ mean motion in the vertical along-track plane below flight level is synthesized using one radar antenna pointing to nadir, and one 30° forward of nadir. This yields instantaneous cross-mountain hydrometeor streamlines. The dynamics of the orographic flow dominate the precipitation patterns across the mountain. Three patterns are distinguished: the first two contain small convective cells, either boundary layer (BL) convection or elevated convection, the latter likely due to the release of potential instability in orographically lifted air. In these patterns the cross-mountain flow is relatively undisturbed. Precipitation from BL convection falls mostly on the windward side but precipitation from elevated convection may fall mostly in the lee. The third pattern is marked by more stratified flow, often with vertically propagating mountain waves, and with strong, plunging flow in the lee, resulting in rapid clearing of the storm across the crest and occasionally a hydraulic jump. In this case, most snow tends to fall upwind of the crest, although a shallow, sublimating snow “foot” is often seen over the leeward slopes.

Robust Aircraft Routing

We propose a robust optimization approach to minimize total propagated delay in the aircraft routing problem, a setting first developed by Lan et al. (2006) and then extended by Dunbar et al. (2012, 2014). Instead of minimizing the expected total propagated delay by assuming that flight leg delays follow specific probability distributions, our model minimizes the maximal possible total propagated delay when flight leg delays lie in a pre-specified uncertainty set. We develop exact and tractable solution approaches for our robust model. The major contribution of our model is that it allows us to explicitly model and handle correlation in flight leg delays (e.g., due to weather or various air traffic management initiatives) that existing approaches cannot efficiently incorporate. Using both historical delay data and simulated data, we evaluate the performance of our model and benchmark against the state-of-the-research stochastic approach (Dunbar et al. 2014). In most of the cases, we observe that our model outperforms the existing approach in lowering the mean, reducing volatility, and mitigating extreme values of total propagated delay. In the cases where a deficit in one of the three criteria exists, gains in the other two criteria usually offset this disadvantage. These results suggest that robust optimization approaches can provide promising results for the aircraft routing problem.

Sleep and sleepiness of pilots operating long-range airplane emergency medical missions.

Airplane emergency medical services (AEMS) operators use fixed-wing airplanes to undertake rapid response, round-the-clock medical transport missions. This paper explores the structure of long-range, multileg AEMS missions and the sleep and sleepiness of the pilots who work them. During nine long-range AEMS missions, pilots kept a sleep and sleepiness logbook and wore a wrist activity monitor to evaluate the timing of sleep/wake. Missions had a mean duration of 20 h 00 min ± 2 h 39 min, involved two to four flight legs, and were crewed by three or four pilots who rotated between operating and sleeping in curtained-off bunks. The pilots obtained a mean of 15 h 26 min ± 4 h 51 min and 7 h 54 min ± 1 h 33 min of sleep in the 48 h and 24 h prior to checking in for duty, respectively. During missions, a mean of 3 h 33 min ± 1 h 46 min of sleep was taken, usually across two in-flight sleep periods. Karolinska Sleepiness Scores (KSS) at top of climb and top of descent were typically less than 5 ('neither alert nor sleepy'). A small number of individual higher KSS scores were recorded on the longest missions and on flights between 02:00 and 06:00. These findings suggest that despite the long duration, timing, and multileg nature of AEMS missions, it is possible via careful design and management to operate these missions with appropriate levels of pilot alertness.

Randomization Approaches for Network Revenue Management with Customer Choice Behavior

In this study, we present new approximation methods for the network revenue management problem with customer choice behavior. Our methods are sampling‐based and so can handle fairly general customer choice models. The starting point for our methods is a dynamic program that allows randomization. An attractive feature of this dynamic program is that the size of its action space is linear in the number of itineraries, as opposed to exponential. It turns out that this dynamic program has a structure that is similar to the dynamic program for the network revenue management problem under the so called independent demand setting. Our approximation methods exploit this similarity and build on ideas developed for the independent demand setting. We present two approximation methods. The first one is based on relaxing the flight leg capacity constraints using Lagrange multipliers, whereas the second method involves solving a perfect hindsight relaxation problem. We show that both methods yield upper bounds on the optimal expected total revenue. Computational experiments demonstrate the tractability of our methods and indicate that they can generate tighter upper bounds and higher expected revenues when compared with the standard deterministic linear program that appears in the literature.

On the incorporation of upgrades into airline network revenue management

Recently, the standard dynamic programming model of network revenue management has been extended for integrated upgrade decision-making. However, opposed to the original model, heuristically breaking the extended model down into a series of single-leg problems by dynamic programming decomposition in order to allow for real-world application is not possible. This is because the model’s state space does not incorporate resources but commitments reflecting already sold products and capacity consumption is only resolved at the end of the booking horizon, thereby considering upgrade options. In this paper, we consider arbitrary airline networks with upgrades being performed separately on each flight leg. We show that in this case, there are two reformulations of the extended model. First, we prove that an ad hoc formulation, in which upgrades are technically performed immediately after a sale, is completely equivalent. Second, we present another reformulation whose idea is adapted from linear programing-based production planning with alternative machine types. We prove that the resulting dynamic program is also equivalent. The advantage of both reformulations is that their state space is based on either real or virtual resources instead of commitments. Thus, dynamic programming decomposition techniques can again be applied. Despite the formal equivalence of both reformulations, applying decomposition techniques leads to different approximations and thus to potentially different results when applied in practice. Therefore, we finally numerically examine the approaches regarding revenue performance and discuss airline revenue management settings in which they differ.

Modeling Upgrades in Airline Revenue Management

Recently, the standard dynamic programming model of network revenue management has been extended for integrated upgrade decision-making. However, opposed to the original model, heuristically breaking the extended model down into a series of single-leg problems by dynamic programming decomposition in order to allow for real-world application is not possible. This is because the model’s state space does not incorporate resources but commitments reflecting already sold products and capacity consumption is only resolved at the end of the booking horizon, thereby considering upgrade options. In this paper, we consider arbitrary airline networks with upgrades being performed separately on each flight leg. We show that in this case, there are two reformulations of the extended model. First, we prove that an ad hoc formulation, in which upgrades are technically performed immediately after a sale, is completely equivalent. Second, we present another reformulation whose idea is adapted from linear programing-based production planning with alternative machine types. We prove that the resulting dynamic program is also equivalent. The advantage of both reformulations is that their state space is based on either real or virtual resources instead of the commitments used in the postponement formulation. Thus, dynamic programming decomposition techniques can again be applied. Despite the formal equivalence of both reformulations, applying decomposition techniques leads to different approximations and thus to potentially different results when applied in practice. Therefore, we finally numerically examine the approaches regarding revenue performance and discuss airline revenue management settings in which they differ.

Aircraft Evaluation of Ground-Based Raman Lidar Water Vapor Turbulence Profiles in Convective Mixed Layers

AbstractHigh temporal and vertical resolution water vapor measurements by Raman and differential absorption lidar systems have been used to characterize the turbulent fluctuations in the water vapor mixing ratio field in convective mixed layers. Since daytime Raman lidar measurements are inherently noisy (due to solar background and weak signal strengths), the analysis approach needs to quantify and remove the contribution of the instrument noise in order to derive the desired atmospheric water vapor mixing ratio variance and skewness profiles. This is done using the approach outlined by Lenschow et al.; however, an intercomparison with in situ observations was not performed.Water vapor measurements were made by a diode laser hygrometer flown on a Twin Otter aircraft during the Routine Atmospheric Radiation Measurement (ARM) Program Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) field campaign over the ARM Southern Great Plains (SGP) site in 2009. Two days with Twin Otter flights were identified where the convective mixed layer was quasi stationary, and hence the 10-s, 75-m data from the SGP Raman lidar could be analyzed to provide profiles of water vapor mixing ratio variance and skewness. Airborne water vapor observations measured during level flight legs were compared to the Raman lidar data, demonstrating good agreement in both variance and skewness. The results also illustrate the challenges of comparing a point sensor making measurements over time to a moving platform making similar measurements horizontally.

Aircraft‐based observations of air–sea turbulent fluxes around the British Isles

Observations of turbulent fluxes of momentum, heat and moisture from low‐level aircraft data are presented. Fluxes are calculated using the eddy covariance technique from flight legs typically ∼40 m above the sea surface. Over 400 runs of 2 min (∼12 km) from 26 flights are evaluated. Flight legs are mainly from around the British Isles although a small number are from around Iceland and Norway. Sea‐surface temperature (SST) observations from two on‐board sensors (the ARIES interferometer and a Heimann radiometer) and a satellite‐based analysis (OSTIA) are used to determine an improved SST estimate. Most of the observations are from moderate to strong wind speed conditions, the latter being a regime short of validation data for the bulk flux algorithms that are necessary for numerical weather prediction and climate models. Observations from both statically stable and unstable atmospheric boundary‐layer conditions are presented. There is a particular focus on several flights made as part of the DIAMET (Diabatic influence on mesoscale structures in extratropical storms) project.Observed neutral exchange coefficients are in the same range as previous studies, although higher for the momentum coefficient, and are broadly consistent with the COARE 3.0 bulk flux algorithm, as well as the surface exchange schemes used in the ECMWF and Met Office models. Examining the results as a function of aircraft heading shows higher fluxes and exchange coefficients in the across‐wind direction, compared to along‐wind (although this comparison is limited by the relatively small number of along‐wind legs). A multi‐resolution spectral decomposition technique demonstrates a lengthening of spatial scales in along‐wind variances in along‐wind legs, implying the boundary‐layer eddies are elongated in the along‐wind direction. The along‐wind runs may not be able to adequately capture the full range of turbulent exchange that is occurring because elongation places the largest eddies outside of the run length.

Changes in leg spring behaviour, plantar loading and foot mobility magnitude induced by an exhaustive treadmill run in adolescent middle-distance runners

This study aimed to determine adjustments in spring-mass model characteristics, plantar loading and foot mobility induced by an exhaustive run. Within-participants repeated measures. Eleven highly-trained adolescent middle-distance runners ran to exhaustion on a treadmill at a constant velocity corresponding to 95% of velocity associated with VO₂max (17.8 ± 1.4 kmh(-1), time to exhaustion=8.8 ± 3.4 min). Contact time obtained from plantar pressure sensors was used to estimate spring-mass model characteristics, which were recorded (during 30 s) 1 min after the start and prior to exhaustion using pressure insoles. Foot mobility magnitude (a composite measure of vertical and medial-lateral mobility of the midfoot) was measured before and after the run. Mean contact area (foot to ground), contact time, peak vertical ground reaction force, centre of mass vertical displacement and leg compression increased significantly with fatigue, while flight time, leg stiffness and mean pressure decreased. Leg stiffness decreased because leg compression increased to a larger extent than peak vertical ground reaction forces. Step length, step frequency and foot mobility magnitude did not change at exhaustion. The stride pattern of adolescents when running on a treadmill at high constant velocity deteriorates near exhaustion, as evidenced by impaired leg-spring behaviour (leg stiffness) and altered plantar loading.

On the Approximate Linear Programming Approach for Network Revenue Management Problems

One method to obtain high-quality bid prices for network revenue management problems involves using the approximate linear programming approach on the dynamic programming formulation of the problem. This approach ends up with a linear program whose number of constraints increases exponentially with the number of flight legs in the airline network. The linear program is solved using constraint generation, where each constraint can be generated by solving a separate integer program. The necessity to solve integer programs and the slow convergence behavior of constraint generation are generally recognized as drawbacks of this approach. In this paper, we show how to effectively eliminate these drawbacks. In particular, we establish that constraint generation can actually be carried out by solving minimum-cost network flow problems with natural integer solutions. Furthermore, using the structure of minimum-cost network flow problems, we a priori reduce the number of constraints in the linear program from exponential to linear in the number of flight legs. It turns out that the reduced linear program can be solved without using separate problems to generate constraints. The reduced linear program also provides a practically appealing interpretation. Computational experiments indicate that our results can speed up the computation time for the approximate linear programming approach by a factor ranging between 13 and 135.

Understanding the Relationships between Lightning, Cloud Microphysics, and Airborne Radar-Derived Storm Structure during Hurricane Karl (2010)

Abstract This study explores relationships between lightning, cloud microphysics, and tropical cyclone (TC) storm structure in Hurricane Karl (16 September 2010) using data collected by the NASA DC-8 and Global Hawk (GH) aircraft during NASA’s Genesis and Rapid Intensification Processes (GRIP) experiment. The research capitalizes on the unique opportunity provided by GRIP to synthesize multiple datasets from two aircraft and analyze the microphysical and kinematic properties of an electrified TC. Five coordinated flight legs through Karl by the DC-8 and GH are investigated, focusing on the inner-core region (within 50 km of the storm center) where the lightning was concentrated and the aircraft were well coordinated. GRIP datasets are used to compare properties of electrified and nonelectrified inner-core regions that are related to the noninductive charging mechanism, which is widely accepted to explain the observed electric fields within thunderstorms. Three common characteristics of Karl’s electrified regions are identified: 1) strong updrafts of 10–20 m s−1, 2) deep mixed-phase layers indicated by reflectivities >30 dBZ extending several kilometers above the freezing level, and 3) microphysical environments consisting of graupel, very small ice particles, and the inferred presence of supercooled water. These characteristics describe an environment favorable for in situ noninductive charging and, hence, TC electrification. The electrified regions in Karl’s inner core are attributable to a microphysical environment that was conducive to electrification because of occasional, strong convective updrafts in the eyewall.