An iterative approach to robust and integrated aircraft routing and crew scheduling

In airline scheduling a variety of planning and operational decision problems have to be solved. We consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights in a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved later. Also, when minimal cost solutions are used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day. We generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We solve the two original problems iteratively. Starting from a minimal cost solution, we produce a series of solutions which are increasingly robust. Using data from domestic airline schedules we evaluate the benefits of the approach as well as the trade-off between cost and robustness. We extend our approach considering the aircraft routing problem together with two crew pairing problems, one for technical crew and one for flight attendants.     

Solving shortest path problems with a weight constraint and replenishment arcs

This paper tackles a generalization of the weight constrained shortest path problem (WCSPP) in a directed network with replenishment arcs that reset the accumulated weight along the path to zero. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests; and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we review the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We present the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications.     

Flight operations recovery: New approaches considering passenger recovery

The sources of disruption to airline schedules are many, including crew absences, mechanical failures, and bad weather. When these unexpected events occur, airlines recover by replanning their operations. In this paper, we present airline schedule recovery models and algorithms that simultaneously develop recovery plans for aircraft, crews, and passengers by determining which flight leg departures to postpone and which to cancel. The objective is to minimize jointly airline operating costs and estimated passenger delay and disruption costs. This objective works to balance these costs, potentially increasing customer retention and loyalty, and improving airline profitability. Using an Airline Operations Control simulator that we have developed, we simulate several days of operations, using passenger and flight information from a major US airline. We demonstrate that our decision models can be applied in a real-time decision-making environment, and that decisions from our models can potentially reduce passenger arrival delays noticeably, without increasing operating costs.     

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

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

Robust crew pairing for managing extra flights

This paper discusses a modeling approach to robust crew pairing when a set of extra flights is likely to be added to the regular flight schedule. The set of these possible extra flights is known at the planning stage. We demonstrate that these extra flights may be incorporated into the schedule if necessary by modifying the planned crew pairings appropriately and without delaying or canceling existing flights. To this end, we either identify a pair of crews whose schedules may be (partially) swapped while adding an extra flight into the schedule or show that an extra flight may be inserted into the schedule of a crew without affecting others. We note that deadheading may be necessary in either case. For these two types of solutions, we define the appropriate feasibility rules with respect to the common airline regulations. We then propose two robust mathematical programming models that consider incorporating such solutions into the set of selected pairings while keeping the increase in the crew cost at an acceptable level. The baseline solution for comparison is found by a conventional crew pairing model in the literature which ignores robustness at the planning stage and relies on recovery procedures at the time of operation. We also propose the variations of the two models, where the double counting of the possible solutions across extra flights is prevented. Finally, we conduct computational experiments on a set of data generated from the actual data of an airline company. We solve the crew pairing problem both with the proposed robust models and the conventional model. Our results demonstrate the benefits of the proposed modeling approach and indicate that the proposed robust models provide natural options to recovery without disrupting the existing flights at a relatively small incremental cost, which is visible at the planning stage.     

Improving Airline Network Robustness and Operational Reliability by Sequential Optimisation Algorithms

A sequential optimisation algorithm is developed to improve the operational reliability of airline schedules. Simulation results show that departure delays are reduced by 30% after optimisation by using extra 260 min buffer times in the schedule. This also increases the network-wide schedule reliability from 37 to 52% and an estimated delay cost saving of $20 million dollars per annum for a small airline network. The advantage of sequential optimisation is that it considers the delay/punctuality propagation in airline networks, so to prevent airlines from planning excessive buffer times to individual flights by considering aircraft rotation as a whole process.     

A two stage heuristic algorithm for the integrated aircraft and crew schedule recovery problems

Airline disruptions incurred huge cost for airlines and serious inconvenience for travelers. In this paper, we study the integrated aircraft and crew schedule recovery problem. A two stage heuristic algorithm for the integrated recovery problem is proposed. In the first stage, the integrated aircraft recovery and flight-rescheduling model with partial crew consideration is built. This model is based on the traditional multi-commodity network model for the aircraft schedule recovery problem. The objective of this model also includes minimization of the original crew connection disruption. In the second stage, the integrated crew schedule recovery and flight re-scheduling model with partial aircraft consideration is built. We proposed a new multi-commodity model for the crew schedule recovery. The main advantage of such model is that it is much more efficient to integrate the flight-scheduling and aircraft consideration. New constraints are incorporated to guarantee that the aircraft connections generated in the stage 1 are still feasible. Two stages are run iteratively until no improvement can be achieved. Experimental results show that our method can provide better recovery solutions compared with the benchmark algorithms.     

航班延误树的构造与波及分析

由于一架飞机在一天中要执行多个航班,各航班之间存在前后衔接关系,因此,一个航班的延误会波及到下游许多其它航班。重点研究飞机和机组资源对于航班延误与波及的影响,给出延误树的生成过程,通过初始航班延误的触发,动态建立以该航班为根结点的航班延误树,并根据统计结果给出相关量值。实例分析了初始航班延误发生的时刻、持续时间与波及的程度,以期辅助优化飞机与机组排班,减少航班延误。     

A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem

The integrated aircraft routing and crew scheduling problem consists in determining a minimum-cost set of aircraft routes and crew pairings such that each flight leg is covered by one aircraft and one crew, and side constraints are satisfied. While some side constraints involve only crews or aircraft, linking constraints impose minimum connection times for crews that depend on aircraft connections. We propose an enhanced model incorporating robustness to handle these linking constraints and compare two Benders decomposition methods—one with the aircraft routing problem as the master problem and one with the crew pairing problem. We also study the impact of generating Pareto-optimal cuts on the speed of convergence of these methods. Computational experiments performed on test instances provided by two major airlines show that the proposed approach yields high-quality solutions in reasonable computing times.     

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.     

Agent-based airline scheduling

The development of an airline schedule can be defined as the art of developing system-wide flight patterns that deliver optimum service to the public in terms of quantity as well as quality. The development of the schedule is market driven with maintenance and crew requirements as constraints. This paper deals with an integrated agent-based approach for the airline scheduling problem. A bidding protocol is used to generate a market based schedule. FIFO and genetic algorithms are used to develop a crew schedule. An expert system combined with the Q-learning algorithm assist operational schedulers in resolving operational conflicts such as delays.     

Disruption management in the airline industry—Concepts,models and methods

This paper provides a thorough review of the current state-of-the-art within airline disruption management of resources, including aircraft, crew, passenger and integrated recovery. An overview of model formulations of the aircraft and crew scheduling problems is presented in order to emphasize similarities between solution approaches applied to the planning and recovery problems. A brief overview of research within schedule robustness in airline scheduling is included in the review, since this proactive measure is a natural complement to disruption management.     

An integrated aircraft routing,crew scheduling and flight retiming model

In the integrated aircraft routing, crew scheduling and flight retiming problem, a minimum-cost set of aircraft routes and crew pairings must be constructed while choosing a departure time for each flight leg within a given time window. Linking constraints ensure that the same schedule is chosen for both the aircraft routes and the crew pairings, and impose minimum connection times for crews that depend on aircraft connections and departure times. We propose a compact formulation of the problem and a Benders decomposition method with a dynamic constraint generation procedure to solve it. Computational experiments performed on test instances provided by two major airlines show that allowing some flexibility on the departure times within an integrated model yields significant cost savings while ensuring the feasibility of the resulting aircraft routes and crew pairings.     

基于二次遗传算法的机组任务配对问题研究

机组任务配对是机组排班问题中主要的一个子问题,发现一组往返飞行航线并且覆盖所有的航班,最重要的是要求运营成本最低.在机组任务选择阶段和机组任务配对阶段采用二次遗传算法,建立了机组任务配对数学模型.根据遗传算法设计,对某航空公司某基地排班的航班信息进行了实例分析,并给出了测试结果.结果说明二次遗传算法在机组任务配对问题中可以寻找到一个更优的解.     

Airline flight schedule planning under competition

This paper presents a modeling framework for airline flight schedule planning under competition. The framework generates an operational flight timetable that maximizes the airline's revenue, while ensuring efficient utilization of the airline's resources (e.g. aircraft and crew). It explicitly considers passenger demand shift due to the network-level competition with other airlines. It also considers minimizing the needless ground time of the resources. The problem is formulated in the form of a bi-level mathematical program where the upper level represents the airline scheduling decisions, while the lower level captures passenger responses in terms of itinerary choices. A solution methodology is developed which integrates a meta- heuristic search algorithm, a network competition analysis model, and a resource (e.g. aircraft and crew) tracking model. The performance of the framework is evaluated through several experiments to develop the schedule for a major U.S. airline. The results demonstrate the success of the framework to develop a competitive schedule with efficient resources.     

Solving a robust airline crew pairing problem with column generation

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness in this case is related to the ability of accommodating these extra flights at the time of operation by disrupting the original plans as minimally as possible. We focus on the crew pairing aspect of robustness and prescribe that the planned crew pairings incorporate a number of predefined recovery solutions for each potential extra flight. These solutions are implemented only if necessary for recovery purposes and involve either inserting an extra flight into an existing pairing or partially swapping the flights in two existing pairings in order to cover an extra flight. The resulting mathematical programming model follows the conventional set covering formulation of the airline crew pairing problem typically solved by column generation with an additional complication. The model includes constraints that depend on the columns due to the robustness consideration and grows not only column-wise but also row-wise as new columns are generated. To solve this difficult model, we propose a row and column generation approach. This approach requires a set of modifications to the multi-label shortest path problem for pricing out new columns (pairings) and various mechanisms to handle the simultaneous increase in the number of rows and columns in the restricted master problem during column generation. We conduct computational experiments on a set of real instances compiled from local airlines in Turkey.     

Duty-period-based network model for crew rescheduling in European airlines

Airline rescheduling is a relatively new field in airline Operations Research but increasing amounts of traffic will make disturbances to the original schedule more frequent and more severe. Thus, the need to address the various problems arising from this situation with systematic, cost-efficient approaches is becoming more urgent. One such problem is crew rescheduling where after a disturbance in the crew schedule the aim is to determine new crew assignments that minimize the `impact’ on the original schedule. In this work we present a new duty-period-based formulation for the airline crew rescheduling problem that is tailored to the needs of European airlines. It uses a new type of resource constraints to efficiently cover the various labor regulations. A solution method based on branch-and-price is tested on various rescheduling scenarios, each with several distinct cases. Results show that the solution method is capable of providing solutions within the short period of time available to a rescheduler after a disturbance occurs.     

Aircrew pairings with possible repetitions of the same flight number

A crew pairing is a sequence of flights, connections and rests that starts and ends at a crew base and is assigned to a single crew. The crew pairing problem consists of determining a minimum cost set of feasible crew pairings such that each flight is covered exactly once and side constraints are satisfied. Traditionally, this problem has been solved in the industry by a heuristic three-phase approach that solves sequentially a daily, a weekly, and a monthly problem. This approach prohibits or strongly penalizes the repetition of the same flight number in a pairing. In this paper, we highlight two weaknesses of the three-phase approach and propose alternative solution approaches that exploit flight number repetitions in pairings. First, when the flight schedule is irregular, we show that better quality solutions can be obtained in less computational time if the first two phases are skipped and the monthly problem is solved directly using a rolling horizon approach based on column generation. Second, for completely regular flight schedules, we show that better quality solutions can be derived by skipping the daily problem phase and solving the weekly problem directly.     

考虑多车场出退勤的城轨交通乘务任务配对模型及算法

针对多个出退勤车场的城市轨道交通线路,研究乘务任务配对问题的数学模型和算法,在满足各车场出退勤任务守恒的前提下,尽可能提高整体值乘效率.首先,考虑出退勤约束、轮换约束、用餐约束和工作量约束,构建任务段衔接网络有向图,并设计广度搜索算法搜寻满足各班种要求的候选任务池.然后,在此基础上,以乘务总值乘费用最小为目标,构建乘务任务配对问题的集覆盖模型.接着,为了提高大规模问题的求解效率,设计基于列生成思想的启发式求解算法.最后,以南昌地铁1号线为例,通过实例验证发现:所提出方法能够合理安排早班和夜班任务的出、回场方式,很好地满足了各车场夜、早任务守恒需求;相对于现行方案,有效减少了两个乘务任务,且任务段平均衔接时间减少了1分17秒;所提出模型和算法能够满足多车场出退勤需求,且保证了值乘效率,能够为实际运营提供决策支持.     

Optimizing railway crew schedules with fairness preferences

Railway crew scheduling deals with generating duties for train drivers to cover all train movements of a given timetable while taking into account a set of work regulations. The objective is to minimize the overall costs associated with a crew schedule, which includes workforce costs and hotel costs. A cost minimal schedule often contains duties that are unpopular to train drivers, and these unpopular duties are often unevenly distributed among crew depots. At the company that motivated our research, for example, train drivers dislike duties that start in the early morning hours. Currently, some crew depots operate large numbers of these unpopular duties, while others do not have any unpopular duties at all. The train drivers perceive this situation as unfair. They prefer schedules with fewer and more evenly distributed unpopular duties across crew depots. In this paper, we define and measure unpopularity and (un)fairness in a railway crew scheduling context. We integrate fairness conditions into a column generation-based solution algorithm and analyze the effect of increased fairness on cost. We also show how increased fairness affects the unpopularity of a schedule. Our method has been applied to test instances at a large European railway freight carrier. Compared to a standard approach that penalizes only the number of unpopular duties in a schedule, we were able to significantly improve schedule fairness with only marginal increases in schedule cost.