Aircraft Routing Problem Research Articles

The integrated aircraft routing problem with optional flights and delay considerations

In this paper, we integrate flight scheduling, fleet assignment, and aircraft routing decisions, which are the most prominent decisions in airline planning, while considering the stochasticity of the demand. In addition, optional flights, delays and deadhead flights are considered as they are crucial elements that significantly affect airline profits. Due to the complexity of the formulated problem, three different column generation-based algorithms are developed. The results show that our algorithms can solve the problem in a fraction of the time a commercial solver takes with an optimality gap of less than 0.1%.

Robust integrated maintenance aircraft routing and crew pairing

Given a daily flight schedule and a set of aircraft fleets, the integrated aircraft routing and crew scheduling problem requires finding a maintenance feasible set of aircraft routes and crew pairings such that each individual flight is covered by exactly one aircraft route and one crew pairing. Although these problems are interdependent, they have been traditionally solved sequentially, where the aircraft routing problem, which is solved first, defines a set of periodic aircraft rotations that impose some restrictions on short connections that are subsequently accommodated by the crew pairing problem. A major drawback of this sequential approach is that it ignores most of the interdependencies between the two problems. In particular, it fails to build robust solutions that are resilient to unpredictable disruptions (like adverse weather, aircraft breakdowns, etc.) that translate into delayed and canceled flights. In this paper, we propose an integrated robust model that incorporates the aircraft routing and crew pairing problems within a single framework that aims at generating aircraft routes that are both robust and cost-effective while accommodating technical constraints. A peculiar feature of the proposed model is that it includes a polynomial number of variables and constraints. We solve the resulting integrated model by using a general-purpose solver. Computational results obtained by using data from major airlines demonstrate the benefits of the proposed robust model.

Robust optimization: Lessons learned from aircraft routing

Building robust airline scheduling models involves constructing schedules and routes with reduced levels of flight delays as well as fewer passenger and crew disruptions. In this paper, we study different classes of models to achieve robust airline scheduling solutions, with a focus on the aircraft routing problem. In particular, we compare one domain-specific approach and two general paradigms of robust models, namely, (i) an extreme-value based or robust optimization-based approach, and (ii) a chance-constrained or stochastic optimization-based approach. Our modeling and solution approach demonstrates the creation of data-driven uncertainty sets for aircraft routing using domain-specific knowledge and develops a completely data-driven simulation-based validation and testing approach. We first demonstrate that additional modeling, capturing domain knowledge, is required to adapt these general robust modeling paradigms to the aircraft routing problem, in order to meaningfully add robustness features specific to aircraft routing. However, we show that these models in their naive forms, still face issues of tractability and solution quality for the large-scale networks which are representative of real-world airline scheduling problems. Therefore, we develop and present advanced models that address these shortcomings. Our advanced models can be applied to aircraft routing in multiple ways, through varied descriptions of the uncertainty sets; and moreover, are generally applicable to linear and binary integer programming problems. Through our detailed computational results, we compare the performance of solutions arising from these different robust modeling paradigms and discuss the underlying reasons for their performance differences from a data-driven perspective.

Human performance and strategies while solving an aircraft routing and sequencing problem: an experimental approach

As airport resources are stretched to meet increasing demand for services, effective use of ground infrastructure is increasingly critical for ensuring operational efficiency. Work in operations research has produced algorithms providing airport tower controllers with guidance on optimal timings and sequences for flight arrivals, departures, and ground movement. While such decision support systems have the potential to improve operational efficiency, they may also affect users’ mental workload, situation awareness, and task performance. This work sought to identify performance outcomes and strategies employed by human decision makers during an experimental airport ground movement control task with the goal of identifying opportunities for enhancing user-centered tower control decision support systems. To address this challenge, thirty novice participants solved a set of vehicle routing problems presented in the format of a game representing the airport ground movement task practiced by runway controllers. The games varied across two independent variables, network map layout (representing task complexity) and gameplay objective (representing task flexibility), and verbal protocol, visual protocol, task performance, workload, and task duration were collected as dependent variables. A logistic regression analysis revealed that gameplay objective and task duration significantly affected the likelihood of a participant identifying the optimal solution to a game, with the likelihood of an optimal solution increasing with longer task duration and in the less flexible objective condition. In addition, workload appeared unaffected by either independent variable, but verbal protocols and visual observations indicated that high-performing participants demonstrated a greater degree of planning and situation awareness. Through identifying human behavior during optimization problem solving, the work of tower control can be better understood, which, in turn, provides insights for developing decision support systems for ground movement management.

Robust Optimization: Lessons Learned from Aircraft Routing

Building robust airline scheduling models involves constructing schedules and routes with reduced levels of flight delays as well as fewer passenger and crew disruptions. In this paper, we study different classes of models to achieve robust airline scheduling solutions, with a focus on the aircraft routing problem. In particular, we compare one domain-specific approach and two general paradigms of robust models, namely, (i) an extreme-value based or robust optimization-based approach, and (ii) a chance-constrained or stochastic optimization-based approach. Our modeling and solution approach demonstrates the creation of data-driven uncertainty sets for aircraft routing using domain-specific knowledge and develops a completely data-driven simulation-based validation and testing approach. We first demonstrate that additional modeling, capturing domain knowledge, is required to adapt these general robust modeling paradigms to the aircraft routing problem, in order to meaningfully add robustness features specific to aircraft routing. However, we show that these models in their naive forms, still face issues of tractability and solution quality for the large-scale networks which are representative of real-world airline scheduling problems. Therefore, we develop and present advanced models that address these shortcomings. Our advanced models can be applied to aircraft routing in multiple ways, through varied descriptions of the uncertainty sets; and moreover, are generally applicable to linear and binary integer programming problems. Through our detailed computational results, we compare the performance of solutions arising from these different robust modeling paradigms and discuss the underlying reasons for their performance differences from a data-driven perspective.

A Novel Model and Decomposition Approach for the Integrated Airline Fleet Assignment, Aircraft Routing, and Crew Pairing Problem

Given a daily flight schedule and a set of aircraft fleets, the airline scheduling problem assigns individual aircraft and groups of crew to each flight based on specific considerations of aircraft maintenance requirements and crew work rules, respectively. Traditionally, this problem has been sequentially broken down into several stages, where the fleet assignment problem, which is solved first, partitions the entire flight network into subnetworks according to fleet types, followed by respectively solving the aircraft routing and crew pairing problems to generate suitable aircraft and crew rotations. However, this sequential approach ignores the interdependencies among the stages, leading to suboptimal, or even infeasible, solutions. In this paper, we propose an integrated model and solution approach that incorporates the fleet assignment (with itinerary-based demands), aircraft routing, and crew pairing problems within a single framework. We solve the resulting formulation of the problem by using a Benders decomposition approach, along with several acceleration strategies. Computational results obtained by using real-life data from a major U.S. airline demonstrate the benefits of the integrated approach.

Integrated Aircraft Routing, Crew Pairing, and Tail Assignment: Branch-and-Price with Many Pricing Problems

A significant drawback of the usual sequential airline scheduling approach is the long lead time between solution of the aircraft routing and aircrew planning problems, and the day of operation. We consider a new approach to airline planning, in which aircraft routes and crew pairings are reoptimized close to the day of operations, via solution of an integrated aircraft routing, crew pairing, and tail assignment problem. Instead of scheduling routes for generic aircraft, we generate routes for each, individual, aircraft given its current location, maintenance, and flying history, while also respecting its individual maintenance requirements. New pairings for crews are planned so as to lie within the work periods given in their roster. This allows aircraft routes and pairings to be designed based on more up-to-date information. By solving an integrated problem, the option of increasing robustness of the resulting schedule by keeping crews and aircraft on the same connections when the connection time is not long can be included in the optimization objective. The problem is formulated as a branch-and-price model with a pricing problem (PP) for each aircraft and each group of crews having the same work period availability and base. We develop two strategies to address the challenge of solving the large number of PPs that result. The feasibility of this approach is demonstrated using real airline data from an Australian domestic airline.

Development of Hybrid Algorithm for Integrated Aircraft Routing Problem and Crew Pairing Problem

Traditionally, aircraft routing and crew pairing problems are solved sequentially with the aircraft routing problem solved first followed by the crew pairing problem. But in some cases, the results are suboptimal. In order to overcome this problem, both problems will be composed in one model. Although the integration model is challenging to solve but it is practically useful in airlines operations for getting the optimal solutions. In this study, we proposed the constructive heuristic method and the genetic algorithm (GA) in producing the feasible paths. After that, we will solve those two types of feasible paths in the integrated model by using three approaches which are the integer linear programming (ILP), Dantzig Wolfe decomposition method and Benders decomposition method. Computational results show that the obtained feasible path from the constructive heuristic method and solved by the Dantzig Wolfe decomposition method is more effective while the paths from the GA and solved by the Dantzig Wolfe decomposition method is good in finding the minimum computational time. From the results obtained, all the flight legs and crew pairing are used only once. There are four type of aircrafts are used in testing the performance of the approaches which based on local flights in Malaysia for seven days. The solutions of the feasible paths from GA is more advantageous in term of the computational times compare to the solutions by using the feasible paths from constructive heuristic method.

Application of Multiple-Population Genetic Algorithm in Optimizing the Train-Set Circulation Plan Problem

The train-set circulation plan problem (TCPP) belongs to the rolling stock scheduling (RSS) problem and is similar to the aircraft routing problem (ARP) in airline operations and the vehicle routing problem (VRP) in the logistics field. However, TCPP involves additional complexity due to the maintenance constraint of train-sets: train-sets must conduct maintenance tasks after running for a certain time and distance. The TCPP is nondeterministic polynomial hard (NP-hard). There is no available algorithm that can obtain the optimal global solution, and many factors such as the utilization mode and the maintenance mode impact the solution of the TCPP. This paper proposes a train-set circulation optimization model to minimize the total connection time and maintenance costs and describes the design of an efficient multiple-population genetic algorithm (MPGA) to solve this model. A realistic high-speed railway (HSR) case is selected to verify our model and algorithm, and, then, a comparison of different algorithms is carried out. Furthermore, a new maintenance mode is proposed, and related implementation requirements are discussed.

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 .

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.

An integrated approach for airline scheduling, aircraft fleeting and routing with cruise speed control

To place an emphasis on profound relations among airline schedule planning problems and to mitigate the effect of unexpected delays, we integrate schedule design, fleet assignment and aircraft routing problems within a daily planning horizon while passengers’ connection service levels are ensured via chance constraints. We propose a nonlinear mixed integer programming model due to the nonlinear fuel consumption and CO2 emission cost terms in the objective function, which is handled by second order conic reformulation. The key contribution of this study is to take into account the cruise time control for the first time in an integrated model of these three stages of airline operations. Changing cruise times of flights in an integrated model enables to construct a schedule to increase utilization of fuel efficient aircraft and even to decrease total number of aircraft needed while satisfying the same service level and maintenance requirements for aircraft fleeting and routing. There is a critical tradeoff between the number of aircraft needed to fulfill the required flights and overall operational expenses. We also propose two heuristic methods to solve larger size problems. Finally, computational results using real data obtained from a major U.S. carrier are presented to demonstrate potential profitability in applying the proposed solution methods.

A Heuristic and Exact Method: Integrated Aircraft Routing and Crew Pairing Problem

<p>In airline operations planning, there are four problems which are schedule design, fleet assignment, aircraft routing and crew pairing problem. Those problems are sequentially and interdependent. Aircraft routing and crew pairing problem are hard to solve and normally crew pairing problem dependent to the aircraft routing problem which gives the suboptimal solutions. As minimizing the costs is important in the airline system, so in order to tackle suboptimal solutions, aircraft routing problem and crew pairing problem are being integrated in one model. For solving the integrated model, the feasible aircraft routes and crew pairs are required. Because of that, a method is being proposed in this work for generating the feasible aircraft routes and crew pairs which is the constructive heuristic method. By using the generic aircraft routes and crew pairs, the integrated model then being solve by two approaches. The first approach is the exact method called the integer linear programming (ILP) while the second approach is from the heuristic method called particle swarm optimization. Encouraging results are encountered by testing on four types of aircrafts for one week flight cycle from local flights in Malaysia.</p>

The aircraft routing problem with refueling

In this paper, we present, test, and compare two novel methods to solve the aircraft routing problem with aerial refueling with a multicriteria objective function. We present a mixed-integer linear program (MILP) that utilizes a combination of a network transformation and a formulation that creatively decouples refueling decisions from the nodes within the network. We also present a dynamic program (DP) that, when coupled with an alternative network transformation to account for the multiple criteria within the objective function, applies a node-labeling approach based on a modification of Dijkstra’s algorithm. We test and compare these alternative solution methods on a set of 264 synthetically-generated instances representing 66 combinations of network size and the frequency of aerial refueling point availability. Invoking CPLEX using the C++ callable library to solve the MILP and applying the DP in C++, we found that the application of the DP yields a 98.97 % reduction in the required computational effort, on average, relative to the MILP; the MILP fails to find an optimal solution within a 3,600-s time limit for selected instances of networks having at least 80 nodes and for all instances of networks having at least 350 nodes. In contrast, the DP is more robust than the MILP, as it only requires longer than 3,600 s to solve selected instances of networks having more than 3,000 nodes.

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.

Recoverable robust single day aircraft maintenance routing problem

Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan due to frequent perturbations occurring in operations. There is an emerging concept that focuses on the generation of aircraft routes for a single day to ensure maintenance coverage that night, alleviating the effects of schedule perturbations from preceding days. In this paper, we present a novel approach to ensure that a sufficient number of aircraft routes are provided each day so maintenance critical aircraft receive maintenance that night. By penalising the under supply of routes terminating at maintenance stations from each overnight airport, we construct a single day routing to provide the best possible maintenance plan. This single day aircraft maintenance routing problem (SDAMRP) is further protected from disruptions by applying the recoverable robustness framework. To efficiently solve the recoverable robust SDAMRP acceleration techniques, such as identifying Pareto-optimal cuts and a trust region approach, have been applied. The SDAMRP is evaluated against a set of flight schedules and the results demonstrate a significantly improved aircraft maintenance plan. Further, the results demonstrate the magnitude of recoverability improvement that is achieved by employing recoverable robustness to the SDAMRP.

A Lifted Compact Formulation for the Daily Aircraft Maintenance Routing Problem

Given a set of flights for a specific fleet type, the aircraft routing problem (ARP) determines the flying sequence for each individual aircraft while incorporating specific considerations of minimum turn time, maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenances. This stage is significant to airline companies as it directly assigns operational routes and maintenance breaks for each aircraft in service. Most approaches related to the problem adopt set partitioning formulations that include exponentially many variables, which requires the design of specialized column generation or branch-and-price algorithms and codes. In this paper, we present a compact polynomial-sized representation for the ARP, which is then linearized and lifted using the reformulation-linearization technique. In addition, we propose two root-node strategies for further augmenting the model formulation. The resulting formulations remain polynomial in size, and we show that they can be solved very efficiently by commercial software without complicated algorithmic implementations. The numerical experiments demonstrate high-quality solutions and significant savings in computational time.

Considering Competition to Solve a Flight Schedule and Aircraft Routing Problem for Small Airlines

For the case of low-cost airlines, which are characterized by having a single fleet with a small number of airplanes, in a previous work, a heuristic algorithm (AFS-MRA) was developed to simultaneously find the flight schedule and the aircraft routes subject to maintenance constraints. This work advances this algorithm by incorporating competition in the planning process (MAFS-MRA). Within a time frame with a given demand data, competition is seen as a game with two players (one airline and all its competitors), where the strategies are all the potential origin-destinations that could be included in the flight schedule, and the payment matrix contains the objective function coefficients that depend on the market share and the routes previously selected. Numerical experimentation was undertaken using real data for the case of two airlines that operate at Toluca International Airport in Mexico. It was found that, by considering competition, the occupation improves to 3% and that the number of flights required to satisfy the demand was reduced to 21%. Besides, the updating process reduces the profit computation error in almost 80%, as compared to the real market behavior for the period under study.

Leveraging Fuel Cost Differences in Aircraft Routing by considering Fuel Ferrying Strategies

The focus of this study is on the aircraft routing problem and the potential role of a ferrying strategy for fueling the aircraft. The main contribution is to estimate the cost of maintenance routing when fuel ferrying strategies are considered. A combined model of aircraft routing and fuel management is developed and applied for three scenarios of fuel cost distribution in a small conceptual network with five stations and 18 flight legs. The results show that fuel cost variations make the ferrying strategy effective in the aircraft routing problem.