Integrated Airline Scheduling Research Articles

Competitive integrated airline schedule design and fleet assignment

Airline profits are significantly influenced by competitive timetables that match passenger demand to fleet resources. In this research, we develop an integrated, mixed-integer optimization model to derive a comprehensive flight schedule, fleet assignment, and average airfares jointly. Passenger choice behavior is incorporated through a prospect theory-adjusted, nested, multinomial logit model which estimates market share. The competitive fleet assignment and schedule design (CFSD) formulation is embedded in a differentiated Bertrand game, such that each transport operator optimizes their best response function connected through the market share model. To solve the integrated optimization problem efficiently, a hybrid algorithm is developed that combines stabilized column generation with a large neighborhood search algorithm.The game-theoretic framework is applied to a case study in China involving legacy airlines, a low-cost carrier, and a high-speed rail (HSR) operator. The equilibrium outcomes suggest that the low-cost carrier is likely to stimulate demand and improve the level of service through secondary airports. The further development of high-speed rail service is expected to intensify competition among airlines and reduce the overall fare level. The low-cost carriers and HSR are able to significantly increase overall consumer surplus, providing insights into the potential for low-cost service in the Chinese aviation markets and the entrance of the public service obligation program at minimum cost.

Passenger-Centric Integrated Airline Schedule and Aircraft Recovery

Airlines are known to compete for passengers, and airline profitability heavily depends on the ability to estimate passenger demand, which in turn depends on flight schedules, fares, and the number of seats available at each fare, across all airlines. Interestingly, such competitive interactions and passenger substitution effects may not be limited to the planning stages. Existing regulations in some countries and regions impose monetary compensations to passengers in case of disruptions, altering the way they perceive the utility of other travel alternatives after the disruption starts. These passenger rights regulations may act as catalysts of passengers’ response to recovered schedules. Ignoring such passenger response behavior under operational disruptions may lead airlines to develop subpar recovery schedules. We develop a passenger response model and embed it into a novel integrated optimization approach that recovers airline schedules, aircraft, and passenger itineraries while endogenizing the impacts of airlines' decisions on passenger compensation and passenger response. We also develop an original solution approach, involving exact linearization of the nonlinear passenger cost terms, combined with delayed constraint generation for ensuring aircraft maintenance feasibility and an acceleration technique that penalizes deviations from planned schedules. Computational results on real-world problem instances from two major European airlines are reported, for scenarios involving disruptions, such as delayed flights, airport closures, and unexpected grounding of aircraft. Our approach is found to be tractable and scalable, producing solutions that are superior to airline’s actual decisions and highly robust in the face of passenger response uncertainty. Of particular relevance to the practitioners, our simulation results highlight that accounting for passengers’ disruption response behaviors, even in a highly approximate manner, yields significant benefits to the airline compared with not accounting for them at all, which is the current state-of-the-art. Funding: This work was supported by the Agencia Estatal de Investigación [Grant PID2020-112967GB-C33], the Ministerio de Economía y Competitividad, Spain [Grant TRA2016-76914-C3-3-P], and the Ministerio de Ciencia, Innovación y Universidades, Spain [Grant CAS19/00036].

Choice-Based Airline Schedule Design and Fleet Assignment: A Decomposition Approach

We study an integrated airline schedule design and fleet assignment model for constructing schedules by simultaneously selecting from a pool of optional flights and assigning fleet types to these scheduled flights. This is a crucial tactical decision that greatly influences airline profits. As passenger demand is often substitutable among available fare products (defined as a combination of an itinerary and a fare class) between the same origin–destination pair, we present an optimization approach that includes a passenger choice model for fare product selections. To tackle the formidable computational challenge of solving this large-scale network design problem, we propose a decomposition approach based on partitioning the flight network into smaller subnetworks by exploiting weak dependencies in network structure. The decomposition relies on a series of approximation analyses and a novel fare split problem to allocate optimally the fares of products that are shared by flights in different subnetworks. We present several reformulations that represent fleet assignment and schedule decisions and formally characterize their relative strengths. This gives rise to a new reformulation that is able to trade off strength and size flexibly. We conduct detailed computational experiments using two realistically sized airline instances to demonstrate the effectiveness of our approach. Under a simulated passenger booking environment with both perfect and imperfect forecasts, we show that the fleeting and scheduling decisions informed by our approach deliver significant and robust profit improvement over all benchmark implementations and previous models in the literature.

A matheuristic for the robust integrated airline fleet assignment, aircraft routing, and crew pairing problem

We address an integrated airline scheduling problem that combines three airline planning processes: fleet assignment, aircraft routing, and crew pairing. For a given daily flight schedule, the problem requires simultaneously assigning aircraft and crews to each scheduled flight, taking into account aircraft maintenance restrictions and crew work rules. We propose to solve this complex problem of integrated flight planning while taking into account robustness considerations. In this regard, robustness is achieved by restricting tight connections in the schedule and increasing the number of connections where crews follow the aircraft. We formulate the problem using a very large-scale, yet compact, mixed-integer programming model, and we propose a matheuristic consisting of a decomposition approach and a proximity search algorithm. Computational experiments carried out on real instances from a major airline and having up to 14,014 itineraries, 646 flights, and 202 aircraft provide evidence of the proposed approach’s efficacy. In particular, we find that the average deviation from a conservative bound is at most equal to 0.6%.

Passenger-Centric Integrated Airline Schedule and Aircraft Recovery

Airlines are known to compete for passengers, and airline profitability heavily depends on the ability to estimate passenger demand, which in turn depends on flight schedules, fares and the number of seats available at each fare, across all airlines. Interestingly, such competitive interactions and passenger substitution effects may not be limited to planning stages. Existing regulations in some countries and regions impose monetary compensations to passengers in case of disruptions, altering the way they perceive the utility of other travel alternatives after the disruption starts. These passenger rights regulations may act as catalysts of passengers’ response to recovered schedules. Ignoring such passenger response behavior under operational disruptions may lead airlines to develop subpar recovery schedules. We develop a passenger response model and embed it into a novel integrated optimization approach that recovers airline schedules, aircraft, and passenger itineraries while endogenizing the impacts of airlines' decisions on passenger compensation and passenger response. We also develop an original solution approach, involving exact linearization of the nonlinear passenger cost terms, combined with delayed constraint generation for ensuring aircraft maintenance feasibility and an acceleration technique that penalizes deviations from planned schedules. Computational results on real-world problem instances of a major Spanish airline are reported, for scenarios involving disruptions, such as delayed flights and airport closures. Our solutions are found to be tractable, superior to airline’s actual decisions, and highly robust in the face of passenger response uncertainty. Of particular relevance to the practitioners, our simulation results highlight that accounting for passengers’ disruption response behaviors – even in a highly approximate manner – yields significant benefits to the airline, as compared to not accounting for them at all, which is the current state-of-the-art.

A heuristic approach for optimal integrated airline schedule design and fleet assignment with demand recapture

Flight schedule design and fleet assignment are the two main elements of the airline scheduling process, which have the highest effect on cost and revenue. Although mixed-integer linear programming models were developed for integrated schedule design and fleet assignment, it has been shown that this approach was not efficient for large-scale models. Therefore, this paper aimed at developing a parallel master–slave Genetic Algorithm (PMS-GA) for solving the integrated flight schedule design and fleet assignment problem with demand recapture, particularly for large-scale problems. The integrated schedule design and fleet assignment problem was solved by the master GA, while the slave GA nested inside the master GA solved passenger flow adjustment problem. Considering the complexities of a large-scale integrated problem, we (1) proposed an innovative approach for creating feasible suboptimal initial population, (2) developed customized genetic operators to improve the performance of the PMS-GA compared to the conventional GAs, and (3) implemented migration and repopulation to prevent premature convergence. PMS-GA was tested on seven models with small-, medium-, and large-scales, and the results were compared with the gold-standard mixed-integer linear programming in terms of cost and runtime. The comparative study showed that the PMS-GA achieved suboptimal solutions with costs only 1.8% to 3.0% different than the optimal solution for medium- and large-scale models. However, these solutions were obtained in significantly shorter runtimes (over 500% to 1000%) compared to the mixed-integer linear programming. Also, the results showed that in contrast to the mixed-integer linear programming approach, runtimes of the proposed PMS-GA are highly predictable as a function of the problem size. Our results showed the importance of PMS-GA for integrated schedule design and fleet assignment, particularly for solving large-scale re-scheduling problems in a short time.

Choice-Based Airline Schedule Design and Fleet Assignment: A Decomposition Approach

We study an integrated airline schedule design and fleet assignment model for constructing schedules by simultaneously selecting from a pool of optional flights and assigning fleet types to these scheduled flights. This is a crucial tactical decision which greatly influences airline profit. As passenger demand is often substitutable among available fare products between the same origin-destination pair, we study an optimization model that integrates within it a passenger choice model for fare product selections. To tackle the formidable computational challenge of solving this large-scale network design problem, we propose a decomposition approach based on partitioning the flight network into smaller subnetworks by exploiting weak dependency in the network structure. The decomposition relies on a series of approximation analyses and a novel fare split problem to reliably measure the approximation quality introduced by the partition by optimally allocating fares of products shared by flights in different subnetworks. We present several reformulations by representing fleet assignment and schedule decisions using composite variables and formally characterize the relationship of their strengths. This gives rise to a new reformulation that is able to flexibly trade off strength and size. We conduct detailed computational experiments using two realistically sized airline instances to demonstrate the effectiveness of our approach. Under a simulated passenger booking environment with both perfect and imperfect forecasts, we show that the fleeting and scheduling decisions informed by our approach deliver significant and robust profit improvement over benchmark implementations and previous models in the literature.

Heuristic approaches for flight retiming in an integrated airline scheduling problem of a regional carrier

Flight retiming in airline scheduling consists in slightly modifying the scheduled departure time of some flights with the goal of providing a better service with a cheaper cost. In this research, the departure times must be selected from a small discrete set of options. The whole problem embeds flight retiming, fleet assignment, aircraft routing and crew pairing. Thus, the aim is to determine the departure times of the flights, the fleet assignment and the minimum cost aircraft and crew routes. The objective function takes into account a large cost associated with each crew member, a penalization for short or long connection times, a cost for crew members changing aircraft along their routes, and a minor penalty associated with the use of each aircraft. The constraints enforce aircraft maintenance and crew working rules. In this setting, flight retiming is allowed to potentially reduce the total costs and increase the robustness of the solution against delays by decreasing the number of aircraft changes.We propose and compare four heuristic algorithms based on a Mixed Integer Linear Programming model for the whole problem. The model contains path variables representing the crew pairings, and arc variables representing the aircraft routes. In the heuristic algorithms, column generation is applied on the path variables, and different flight retiming options are considered. The algorithms are tested on real-world instances of a regional carrier flying in the Canary Islands to evaluate their advantages and drawbacks. In particular, one of the algorithms, that uses the solution of the Linear Programming relaxation of the model to select promising options for the departure of the flights, turns out to be the most effective one. The obtained results show that costs can be significantly reduced through flight retiming while still keeping the computing times reasonably short. In addition, we perform a sensitivity analysis by including more retiming options and by using different aircraft and crew costs. Finally, we report the results on larger size instances obtained by combining real-world ones.

Integrated Airline Scheduling: Considering Competition Effects and the Entry of the High Speed Rail

Airlines and high speed rail are increasingly competing for passengers, especially in Europe and Asia. Competition between them affects the number of captured passengers and, therefore, revenues. We consider competition between airlines (legacy and low-cost) and high speed rail. We develop a new approach that generates airline schedules using an integrated mixed integer, nonlinear optimization model that captures the impacts of airlines’ decisions on passenger demand. We estimate the demand associated with a given schedule using a nested logit model. We report our computational results on realistic problem instances of the Spanish airline IBERIA and show that the actual airline schedules are found to be reasonably close to the schedules generated by our approach. Next, we use this optimization modeling approach under multimodal competition to evaluate multiple scenarios involving entry of high speed rail into new markets. We account for the possibility of demand stimulation as a result of the new services. We validate our approach using data from markets that had an entry by high speed rail in the past. The out-of-sample validation results show a close match between the predicted and observed solutions. Finally, we use our validated model to predict the impacts of future entry by high speed rail in new markets. Our results provide several interesting and useful insights into the schedule changes, fleet composition changes, and fare changes that will help the airline cope effectively with the entry of high speed rail.

Optimal Solutions to a Real-World Integrated Airline Scheduling Problem

We study an integrated airline scheduling problem for a regional carrier. It integrates three stages of the planning process (i.e., fleet assignment, aircraft routing, and crew pairing) that are typically solved in sequence. Aircraft maintenance is also taken into account. The objective function aims at minimizing a weighted sum of the number of aircraft routes, the number of crew pairings, and the waiting times of crews between consecutive flights. In addition, it aims at maximizing the robustness of the solution by also minimizing the number of times that crews need to change aircraft. We present two mixed integer linear programming models for the integrated problem. The first formulation, called the path-path model, can be considered as the “natural model” in which both the crew pairings and the aircraft routes are represented by path-based variables. The other formulation, called the arc-path model, is a novel model in which the aircraft routes are represented by arc-based variables and the crew pairings by path-based variables. We propose two exact methods (called path-path method and arc-path method) for solving the integrated problem, each one based on one of the proposed models. Both methods consist of three phases. In the first phase, the linear programming relaxation of the corresponding model is solved to optimality by column generation on the path-based variables, thus providing a lower bound. The second phase computes a heuristic solution (upper bound) by using only the variables generated in the first phase. The third phase makes use of the lower and upper bounds (obtained in the previous phases) to compute an optimal solution. We propose a bounding cut based on computing a lower bound on the number of aircraft changes that are needed in a feasible solution, and empirically show that this cut significantly speeds up the exact methods. The proposed methods are tested on real-world instances of a regional carrier with up to 172 flights and three fleet operators. The results show that the arc-path method outperforms the path-path method as well as a heuristic approach from the literature, and derives the optimal solutions for all of the considered instances in at most two hours of computing time.

A Rolling Horizon Based Algorithm for Solving Integrated Airline Schedule Recovery Problem

A Rolling Horizon Based Algorithm for Solving Integrated Airline Schedule Recovery Problem

An Integrated Airline Scheduling, Fleeting, and Pricing Model for a Monopolized Market

AbstractIn airline schedule planning models, the demand and price information are usually taken as inputs to the model. Therefore, schedule and capacity decisions are taken separately from pricing decisions. In this article, we present an integrated scheduling, fleeting, and pricing model for a single airline where these decisions are taken simultaneously. This integration enables to explicitly model supply and demand interactions and make superior decisions. The model refers to a monopolized market. However, competing airlines are included in the model as a reference for the pricing decisions. The pricing decision is formulated through an itinerary choice model which determines the demand of the alternative itineraries in the same market according to their price, travel time, number of stops, and the departure time of the day. The demand model is estimated based on real data and is developed separately for economy and business classes. The seat allocation for these classes is optimized according to the behavior of the demand. The choice model is also used to appropriately model the spill and recapture effects. The resulting model is evaluated with different illustrations and the added value of the integrated approach is analyzed compared to a sequential approach. Results over a set of representative instances show that the integrated model is able to make superior decisions by jointly adjusting capacity and pricing.

A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture

The airline’s ability to offer flight schedules that provide service to passengers at desired times in competitive markets, while matching demand with an aircraft fleet of suitable size and composition, can significantly impact its profits. In this spirit, optional flight legs can be considered to construct a profitable schedule by optimally selecting among such alternatives in concert with assigning the available aircraft fleet to all the scheduled legs. Examining itinerary-based demands as well as multiple fare-classes can effectively capture network effects and realistic demand patterns. In addition, allowing flexibility on the departure times of scheduled flight legs can increase connection opportunities for passengers, hence yielding robust schedules while saving fleet assignment costs within the framework of an integrated model. Airlines can also capture an adequate market share by balancing flight schedules throughout the day, and recapture considerations can contribute to more realistic accepted demand realizations. We therefore propose in this paper a model that integrates the schedule design and fleet assignment processes while considering flexible flight times, schedule balance, and recapture issues, along with optional legs, path/itinerary-based demands, and multiple fare-classes. A polyhedral analysis is conducted to generate several classes of valid inequalities, which are used along with suitable separation routines to tighten the model representation. Solution approaches are designed by applying Benders decomposition method to the resulting tightened model, and computational results are presented using real data obtained from United Airlines to demonstrate the efficacy of the proposed procedures.

Integrated Airline Schedule Design and Fleet Assignment: Polyhedral Analysis and Benders' Decomposition Approach

The main airline operations consist of schedule planning, fleet assignment, aircraft routing, and crew scheduling. To improve profitability, we present in this paper an integrated fleet assignment model with schedule planning by simultaneously considering optional flight legs to select along with the assignment of aircraft types to all scheduled legs. In addition, we consider itinerary-based demands for multiple fare classes. A polyhedral analysis is conducted of the proposed mixed-integer programming model to tighten its representation via several classes of valid inequalities. Solution approaches are developed by applying Benders' decomposition method to the resulting lifted model, and computational results are presented using real data obtained from a major U.S. airline to demonstrate the efficacy of the proposed procedures.

Integrated airline scheduling

Airline scheduling is composed of fleet assignment, aircraft maintenance routing, and crew scheduling optimization subproblems. It is believed that the full optimization problem is computationally intractable, and hence the constituent subproblems are optimized sequentially so that the output of one is the input of the next. The sequential approach, however, provides an overall suboptimal solution and can also fail to satisfy the maintenance constraints of an otherwise feasible full problem. In this paper several integrated models for the optimization of airline scheduling are presented for the first time, and solved by applying an enhanced Benders decomposition method combined with accelerated column generation. Solutions of several realistic data sets are computed using the integrated models, which are compared with solutions of the best known approaches from the literature. As a result, the integrated approach significantly reduces airline costs. Finally, a comparison of alternative formulations has shown that keeping the crew scheduling problem alone in the Benders subproblem is much more efficient than keeping the aircraft routing problem.