A multi-objective genetic algorithm for robust flight scheduling using simulation

Traditional methods of developing flight schedules generally do not take into consideration disruptions that may arise during actual operations. Potential irregularities in airline operations such as equipment failure are not adequately considered during the planning stage of a flight schedule. As such, flight schedules cannot be met as planned and their performance is compromised, which may eventually lead to huge losses in revenue for airlines. In this paper, we seek to improve the robustness of a flight schedule by re-timing its departure times. The problem is modeled as a multi-objective optimization problem, and a multi-objective genetic algorithm (MOGA) is developed to solve the problem. To evaluate flight schedules, SIMAIR 2.0, a simulation model which simulates airline operations under operational irregularities, has been employed. The simulation results indicate that we are able to develop schedules with better operation costs and on-time performance through the application of MOGA.     

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.     

Constraint Programming Based Column Generation for Crew Assignment

Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.     

单架飞机受干扰后飞机路径恢复多项式算法研究

飞机路径恢复是航班调整中保证航班能够运行的必要条件之一,而传统目标下的飞机路径优化问题是NP-hard的。本文针对单架飞机受到干扰后,基于最小最大目标的同机型飞机路径最优化问题,给出了一个新的多项式时间算法。首先基于航空公司调整航班的常用原则,提出把最大航班延误时间最小化作为问题的目标。然后根据问题的一些特点和目标形式,设计出解构造算法,得到飞机路径恢复问题的最优解,并分析出算法的复杂度为O(n²)。相对于一般的最小最大二分图匹配算法(复杂度为O(n³log(n))),该算法具有较小的时间复杂度。最后用实例验证了解构造算法的有效性。该研究结果将为航空公司减少航班延误提供理论和方法支持。     

A network model for airline cabin crew scheduling

Airline crew scheduling problems have been traditionally formulated as set covering problems or set partitioning problems. When flight networks are extended, these problems become more complicated and thus more difficult to solve. From the current practices of a Taiwan airline, whose work rules are relatively simple compared to many airlines in other countries, we find that pure network models, in addition to traditional set covering (partitioning) problems, can be used to formulate their crew scheduling problems. In this paper, we introduce a pure network model that can both efficiently and effectively solve crew scheduling problems for a Taiwan airline using real constraints. To evaluate the model, we perform computational tests concerning the international line operations of a Taiwan airline.     

Approximate nucleolus-based revenue sharing in airline alliances

Alliances allow the airlines to extend their networks and increase the number of destinations they can access. Different from the traditional single airline approach, in an alliance, partner airlines may sell tickets for the same itinerary. In addition, one itinerary may consist of several flight legs, each of which may be operated by a different airline. A major issue that needs to be addressed is how to share the revenue generated from selling a ticket for a product among the individual airlines in a fair way. The fair allocation of the revenue has a critical importance for the long-term stability of the alliance. We model the problem as a cooperative game and show that the core of the game is non-empty. We propose to use a revenue proration scheme based on the concept of the nucleolus. The numerical studies reveal that the revenue shares can effectively be computed even for large alliance networks.     

中国航空市场占有率的预测与分析

近年来我国航空公司经历了大规模的重组,大大提高了行业的集中度.中国国际航空股份有限公司、中国东方航空股份有限公司、中国南方航空股份有限公司,这三大航空公司几乎垄断了中国的航空市场,而三航之外的中小型航空公司旅客市场占有率较低.因此把三航之外近40家航空公司看做一整体.根据各大航空公司在2008年-2010年的旅客市场占有率数据建立二次规划模型,运用Lingo软件对转移概率矩阵进行估计,预测几大航空公司的旅客市场占有率,并探讨一些初步的改进.通过短期预测,发现未来三大航空公司仍然垄断中国市场.     

A hybrid scatter search heuristic for personalized crew rostering in the airline industry

The crew scheduling problem in the airline industry is extensively investigated in the operations research literature since efficient crew employment can drastically reduce operational costs of airline companies. Given the flight schedule of an airline company, crew scheduling is the process of assigning all necessary crew members in such a way that the airline is able to operate all its flights and constructing a roster line for each employee minimizing the corresponding overall cost for personnel. In this paper, we present a scatter search algorithm for the airline crew rostering problem. The objective is to assign a personalized roster to each crew member minimizing the overall operational costs while ensuring the social quality of the schedule. We combine different complementary meta-heuristic crew scheduling combination and improvement principles. Detailed computational experiments in a real-life problem environment are presented investigating all characteristics of the procedure. Moreover, we compare the proposed scatter search algorithm with optimal solutions obtained by an exact branch-and-price procedure and a steepest descent variable neighbourhood search.     

Fleet assignment and routing with schedule synchronization constraints

This paper introduces a new type of constraints, related to schedule synchronization, in the problem formulation of aircraft fleet assignment and routing problems and it proposes an optimal solution approach. This approach is based on Dantzig–Wolfe decomposition/column generation. The resulting master problem consists of flight covering constraints, as in usual applications, and of schedule synchronization constraints. The corresponding subproblem is a shortest path problem with time windows and linear costs on the time variables and it is solved by an optimal dynamic programming algorithm. This column generation procedure is embedded into a branch and bound scheme to obtain integer solutions. A dedicated branching scheme was devised in this paper where the branching decisions are imposed on the time variables. Computational experiments were conducted using weekly fleet routing and scheduling problem data coming from an European airline. The test problems are solved to optimality. A detailed result analysis highlights the advantages of this approach: an extremely short subproblem solution time and, after several improvements, a very efficient master problem solution time.     

Airline Crew Scheduling: State-of-the-Art

The airline industry is faced with some of the largest scheduling problems of any industry. The crew scheduling problem involves the optimal allocation of crews to flights. Over the last two decades the magnitude and complexity of crew scheduling problems have grown enormously and airlines are relying more on automated mathematical procedures as a practical necessity. In this paper we survey different approaches studied and discuss the state-of-the-art in solution methodology for the airline crew scheduling problem. We conclude with a discussion about promising areas for further work to make it possible to get very good solutions for the crew scheduling problem.     

基于动态列生成算法的飞机排班问题研究

飞机排班是航空运输生产计划的重要环节,对航空公司的正常运营和整体效益有着决定性影响;飞机排班通常构建为大规模整数规划问题,是航空运筹学研究的重要课题,构建的模型属于严重退化的NP-Hard问题.在考虑对多种机型的飞机进行排班时,大大增加了问题的复杂性.针对航空公司实际情况,建立多种机型的飞机排班模型;为实现模型的有效求解,提出了基于约束编程的动态列生成算法;即用约束编程快速求解航班连线(航班串)并计算航班串简约成本,动态选择列集并与限制主问题进行迭代.最后,利用国内某航空公司干线航班网络实际数据验证模型和算法的有效性.     

基于多目标规划的飞机路径恢复最优化算法研究

本文针对同一机场中同机型的多架飞机受到干扰后, 飞机路径恢复的多目标最优化问题进行研究。首先根据航空公司实际航班调整的常用原则和航班干扰管理的基本思想, 基于连接网络建立多目标规划模型, 其中两个目标按照优先级排列:第一个目标为最小化航班的最大延误时间, 第二个目标为最小化参与交换的飞机数量。然后根据该问题的航班波结构特点, 结合求解多目标规划的分层序列法, 分析优化问题的若干最优性质, 并基于快速排序算法和最小费用路算法设计出多项式算法。最后用算例验证了算法的有效性。该研究结果可以为航空公司减少航班延误提供理论和技术支持。     

Airline Base Schedule Optimisation by Flight Network Annealing

A system for rigorous airline base schedule optimisation is described. The architecture of the system reflects the underlying problem structure. The architecture is hierarchical consisting of a master problem for logical aircraft schedule optimisation and a sub-problem for schedule evaluation.The sub-problem is made up of a number of component sub-problems including connection generation, passenger choice modelling, passenger traffic allocation by simulation and revenue and cost determination.Schedule optimisation is carried out by means of simulated annealing of flight networks. The operators for the simulated annealing process are feasibility preserving and form a complete set of operators.     

A Proactive Crew Recovery Decision Support Tool for Commercial Airlines During Irregular Operations

In this paper, a decision support tool that automates crew recovery during irregular operations for large-scale commercial airlines is presented. The tool is designed for airlines that adopt the hub-spoke network stru cture. The advance of this tool over the existing ones is that it recovers projected crew problems that arise due to current system disruptions. In other words, it proactively recovers crew problems ahead of time before their occurrence. In addition, it gives a wide flexibility to react to different operation scenarios. Also, it solves for the most efficient crew recovery plan with the least deviation from the originally planned schedule. The tool adopts a rolling approach in which a sequence of optimization assignment problems is solved such that it recovers flights in chronological order of their departure times. In each assignment problem, the objective is to recover as many flights as possible while minimizing total system cost resulting from resource reassignments and flight delays. The output of this tool is in the form of new crew trippairs that cover flights in the considered horizon. A test case is presented to illustrate the model capabilities to solve a real-life problem for one of the major commercial airlines in the U.S.     

Multifleet routing and multistop flight scheduling for schedule perturbation

Efficient and effective incidental scheduling techniques for schedule perturbation are essential to an airline carrier's operations. This research aims at developing a framework to assist carriers in fleet routing and flight scheduling for schedule perturbations in the operations of multifleet and multistop flights. The framework is based on a basic multifleet schedule perturbation model constructed as a timespace network from which strategic models are developed to research incidental scheduling. These network models are formulated as multiple commodity network flow problems. Lagrangian relaxation with subgradient methods accompanied by the network simplex method, a Lagrangian heuristic and a modified subgradient method are developed to solve the problems. A case study regarding the international operations of a major Taiwan airline carrier is presented.     

Constraint Handling in Genetic Algorithms: The Set Partitioning Problem

In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem (SPP). The SPP is an important combinatorial optimisation problem used by many airlines as a mathematical model for flight crew scheduling.A key feature of the SPP is that it is a highly constrained problem, all constraints being equalities. New genetic algorithm (GA) components: separate fitness and unfitness scores, adaptive mutation, matching selection and ranking replacement, are introduced to enable a GA to effectively handle such constraints. These components are generalisable to any GA for constrained problems.We present a steady-state GA in conjunction with a specialised heuristic improvement operator for solving the SPP. The performance of our algorithm is evaluated on a large set of real-world problems. Computational results show that the genetic algorithm-based heuristic is capable of producing high-quality solutions.     

Wait or buy? The strategic consumer: Pricing and profit implications

Using tools from operations research, airlines have, for many years, taken a strategic approach to pricing the seats available on a particular flight based on demand forecasts and information. The result of this approach is that the same seat on the same flight is often offered at different fares at different times. Setting of these prices using yield-management approaches is a major activity for many airlines and is well studied in the literature. However, consumers are becoming increasingly aware of the existence of pricing strategies used by airlines. In addition, the availability of airline travel pricing on the Internet affords consumers the opportunity to behave more strategically when making purchase decisions. The onset of the information age makes it possible for an informed consumer or a third party, such as a travel agent, to obtain demand information similar to that used by the airlines. In particular, it is possible for consumers or travel agents to purchase historical data or to obtain it by monitoring the seats that are available at various prices for a given flight. If a consumer understands the pricing strategy and has access to demand information, he/she may decide to defer purchase of a ticket because they believe that a cheaper seat may yet become available. If consumers were to make use of this information to make such strategic purchasing decisions, what would be the impact on airline revenues? The purpose of this paper is to investigate these impacts. This work indicates that use of standard yield management approaches to pricing by airlines can result in significantly reduced revenues when buyers are using an informed and strategic approach to purchasing. Therefore, when airlines are setting or presenting prices, they should investigate the effect of strategic purchasing on their decisions.     

An airline scheduling model and solution algorithms under stochastic demands

When setting a good flight schedule airlines not only have to consider their fleet supply and related operations, as well as market share, but also stochastic variations caused by daily passenger demands in actual operations. Most of the past research on short-term flight scheduling has used the average passenger demand as input to produce the final timetable and schedule, which means that daily passenger variations that occur in actual operations are neglected. To consider such stochastic disturbances we developed a stochastic-demand scheduling model. We employed arc-based and route-based strategies to develop two heuristic algorithms that can be used to solve the model. The test results, based on a major Taiwan airline’s operation, show the good performance of the model and the solution algorithms.     

Network capacity management under competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to address the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single-leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.     

Periodic airline fleet assignment with time windows,spacing constraints,and time dependent revenues

Given the sets of flights and aircraft of an airline carrier, the fleet assignment problem consists of assigning the most profitable aircraft type to each flight. In this paper we propose a model for the periodic fleet assignment problem with time windows in which departure times are also determined. Anticipated profits depend on the schedule and the selection of aircraft types. In addition, short spacings between consecutive flights which serve the same origin–destination pair of airports are penalized. We propose a non-linear integer multi-commodity network flow formulation. We develop new branch-and-bound strategies which are embedded in our branch-and-price solution strategy. Finally, we present computational results for periodic daily schedules on three real-world data sets.