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.     

A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases

Crew scheduling for airlines requires an optimally scheduled coverage of flights with regard to given timetables. We consider the crew scheduling and assignment process for airlines, where crew members are stationed unevenly among home bases. In addition, their availability changes dynamically during the planning period due to pre-scheduled activities, such as office and simulator duties, vacancy, or requested off-duty days.We propose a partially integrated approach based on two tightly coupled components: the first constructs chains of crew pairings spaced by weekly rests, where crew capacities at different domiciles and time-dependent availabilities are considered. The second component rearranges parts of these pairing chains into individual crew schedules with, e.g., even distribution of flight time. Computational results with real-life data from an European airline are presented.     

An integrated decision support tool for airlines schedule recovery during irregular operations

This paper presents a decision support tool for airlines schedule recovery during irregular operations. The tool provides airlines control centers with the capability to develop a proactive schedule recovery plan that integrates all flight resources. A rolling horizon modeling framework, which integrates a schedule simulation model and a resource assignment optimization model, is adopted for this tool. The schedule simulation model projects the list of disrupted flights in the system as function of the severity of anticipated disruptions. The optimization model examines possible resource swapping and flight re-quoting to generate an efficient schedule recovery plan that minimizes flight delays and cancellations. A detailed example that illustrates the application of the tool to recover the schedule of a major US air-carrier during a hypothetical ground delay program scenario is presented. The results of several experiments that illustrates overall model performance in terms of solution quality and computation experience are also given.     

Genetic algorithm based approach for the integrated airline crew-pairing and rostering problem

Airline crew scheduling problem is a complex and difficult problem faced by all airline companies.To tackle this problem, it was often decomposed into two subproblems solved successively. First, the airline crew-pairing problem, which consists on finding a set of trips – called pairings – i.e. sequences of flights, starting and ending at a crew base, that cover all the flights planned for a given period of time. Secondly, the airline crew rostering problem, which consists on assigning the pairings found by solving the first subproblem, to the named airline crew members. For both problems, several rules and regulations must be respected and costs minimized.It is sure that this decomposition provides a convenient tool to handle the numerous and complex restrictions, but it lacks, however, of a global treatment of the problem. For this purpose, in this study we took the challenge of proposing a new way to solve both subproblems simultaneously. The proposed approach is based on a hybrid genetic algorithm. In fact, three heuristics are developed here to tackle the restriction rules within the GA’s process.     

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.     

Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods

The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. Given its high complexity, the ICS problem has been traditionally tackled using a sequential two-stage approach, where a crew pairing problem is solved in the first stage and a crew assignment problem in the second stage. Recently, Saddoune et al. (2010b) developed a model and a column generation/dynamic constraint aggregation method for solving the ICS problem in one stage. Their computational results showed that the integrated approach can yield significant savings in total cost and number of schedules, but requires much higher computational times than the sequential approach. In this paper, we enhance this method to obtain lower computational times. In fact, we develop a bi-dynamic constraint aggregation method that exploits a neighborhood structure when generating columns (schedules) in the column generation method. On a set of seven instances derived from real-world flight schedules, this method allows to reduce the computational times by an average factor of 2.3, while improving the quality of the computed solutions.     

Aircrew schedule generation using repeated matching

We consider the Aircrew Scheduling Problem of determining tours of duty (TODs) for aircrews, given a set of sectors (or flights) requiring regular crews. A regular crew consists of two crew members, but by including supplementary crew (a third pilot) on some sectors it is possible to extend duty periods to generate more cost efficient TODS. A related problem is thus to generate TODs for these third pilots, but the sectors requiring a third pilot are not known in advance. To solve these two related problems simultaneously, we apply a heuristic procedure that solves a sequence of matching problems, i.e. a repeated matching algorithm. Numerical results based on the solution of a real problem show that this approach is a valid and efficient method for solving the Aircrew Scheduling Problem, especially when there is the option of using supplementary crew to extend duty periods.     

The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.     

Algorithms for railway crew management

Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a well-known problem in Operations Research and has been historically associated with airlines and mass-transit companies. More recently, railway applications have also come on the scene, especially in Europe. In practice, the overall crew management problem is decomposed into two subproblems, called crew scheduling and crew rostering. In this paper, we give an outline of different ways of modeling the two subproblems and possible solution methods. Two main solution approaches are illustrated for real-world applications. In particular we discuss in some detail the solution techniques currently adopted at the Italian railway company, Ferrovie dello Stato SpA, for solving crew scheduling and rostering problems.     

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.     

Two-level decomposition algorithm for crew rostering problems with fair working condition

A typical railway crew scheduling problem consists of two phases: a crew pairing problem to determine a set of crew duties and a crew rostering problem. The crew rostering problem aims to find a set of rosters that forms workforce assignment of crew duties and rest periods satisfying several working regulations. In this paper, we present a two-level decomposition approach to solve railway crew rostering problem with the objective of fair working condition. To reduce computational efforts, the original problem is decomposed into the upper-level master problem and the lower-level subproblem. The subproblem can be further decomposed into several subproblems for each roster. These problems are iteratively solved by incorporating cuts into the master problem. We show that the relaxed problem of the master problem can be formulated as a uniform parallel machine scheduling problem to minimize makespan, which is NP-hard. An efficient branch-and-bound algorithm is applied to solve the master problem. Effective valid cuts are developed to reduce feasible search space to tighten the duality gap. Using data provided by the railway company, we demonstrate the effectiveness of the proposed method compared with that of constraint programming techniques for large-scale problems through computational experiments.     

Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. We develop a new approach for solving the problem that is based on enumerating hundreds of millions random pairings. The linear programming relaxation is solved first and then millions of columns with best reduced cost are selected for the integer program. The number of columns is further reduced by a linear programming based heuristic. Finally an integer solution is obtained with a commercial integer programming solver. The branching rule of the solver is enhanced with a combination of strong branching and a specialized branching rule. The algorithm produces solutions that are significantly better than ones found by current practice.     

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.     

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.     

考虑地区因素的航空收益管理

对于中国这样一个因地区经济水平不同而造成地区消费差异极度巨大的国家,航空公司应该怎样设置卖票策略使自己的各个航班的效用最大,传统的方法是票价系统因地而异,但这种方法有很大的随意性,并且对订票系统改变较大,操作成本高。本文将采用一个新的方法讨论该问题。首先,引进一个反映地区消费水平的参数,简称地区因子。然后结合一个单阶段航班,建立考虑地区因子的随机动态模型,同时证明了与效用函数相关的一些性质:比例边际效用函数是分别关于时间,待订票数和地区因子的单调增加函数。基于这些性质,对连接不同地域的航班,我们只要调整地区因子,再采用阀值控制策略就能使航班的效用最大且空置率得到有效抑制。最后,给出了一个实例。     

A tree search algorithm for the crew scheduling problem

In this paper we consider the crew scheduling program, that is the problem of assigning K crews to N tasks with fixed start and finish times such that each crew does not exceed a limit on the total time it can spend working.A zero-one integer linear programming formulation of the problem is given, which is then relaxed in a lagrangean way to provide a lower bound which is improved by subgradient optimisation. Finally a tree search procedure incorporating this lower bound is presented to solve the problem to optimality.Computational results are given for a number of randomly generated test problems involving between 50 and 500 tasks.     

Metaheuristics approach for solving personalized crew rostering problem in public bus transit

The crew rostering problem in public bus transit aims at constructing personalized monthly schedules for all drivers. This problem is often formulated as a multi-objective optimization problem, since it considers the interests of both the management of bus companies and the drivers. Therefore, this paper attempts to solve the multi-objective crew rostering problem with the weighted sum of all objectives using ant colony optimization, simulated annealing, and tabu search methods. To the best of our knowledge, this is the first paper that attempts to solve the personalized crew rostering problem in public transit using different metaheuristics, especially the ant colony optimization. The developed algorithms are tested on numerical real-world instances, and the results are compared with ones solved by commercial solvers.     

A model and computational tool for crew scheduling in train transportation of mine materials by using a local search strategy

This work introduces a model of the crew scheduling problem for the operation of trains in the mining industry in the North of Chile. The model possesses particular features due to specific regulations with which train operators in mine material transportation are required to comply: every week, a fixed set of trips must be made according to current demand for the transportation of mine products and supplies. In order to balance the loads of the crews in the long term, the proposed model generates an infinite horizon schedule by means of a rotative scheme in which each crew takes the place of the previous one at the beginning of the next week. This gives rise to a medium/large size 0–1 linear optimization problem, whose solution represents the optimal assignment of drivers to trips with the number of working hours per week distributed equally among crews. The model and algorithm have been implemented with a user interface suitable for the remote execution of real instances on a High Performance Computing platform. The transportation company regularly uses this computerized tool for planning crew schedules and generating efficient assignments for emerging and changing operational conditions.     

Airline crew scheduling from planning to operations

Crew scheduling problems at the planning level are typically solved in two steps: first, creating working patterns, and then assigning these to individual crew. The first step is solved with a set covering model, and the second with a set-partitioning model. At the operational level, the (re) planning period is considerably smaller than during the strategic planning phase. We integrate both models to solve time critical crew recovery problems arising on the day of operations. We describe how pairing construction and pairing assignment are done in a single step, and provide solution techniques based on simple tree search and more sophisticated column generation and shortest-path algorithms.