On air traffic flow management with rerouting. Part II: Stochastic case

We present a framework for modeling multistage mixed 0-1 problems for the air traffic flow management problem with rerouting (ATFMRP) under uncertainty in the airport arrival and departure capacity, the air sector capacity and the flight demand. The model allows for flight cancelation, if necessary. It considers several types of objective functions to minimize, namely, total ground and air holding cost, penalization of the alternative routes to the scheduled one for each flight, delay cost for the flights to arrive to the airports and the air sector nodes, and penalization for advancing the arrival of the flights to the airport over the scheduled period. A scenario tree based scheme is used to represent the Deterministic Equivalent Model (DEM) of the stochastic mixed 0-1 program with full recourse. The nonanticipativity constraints that equate the so named common 0-1 and continuous variables from the same group of scenarios in each period are implicitly satisfied in the compact representation of DEM. Some computational experience is reported for medium-scale instances. The model is so tight that none of the instances of the testbed but two of them requires to execute the branch-and-cut phase of the MIP optimization engine of choice.     

How Airlines and Airports Recover from Schedule Perturbations: A Survey

The explosive growth in air traffic as well as the widespread adoption of Operations Research techniques in airline scheduling has given rise to tight flight schedules at major airports. An undesirable consequence of this is that a minor incident such as a delay in the arrival of a small number of flights can result in a chain reaction of events involving several flights and airports, causing disruption throughout the system. This paper reviews recent literature in the area of recovery from schedule disruptions. First we review how disturbances at a given airport could be handled, including the effects of runways and fixes. Then we study the papers on recovery from airline schedule perturbations, which involve adjustments in flight schedules, aircraft, and crew. The mathematical programming techniques used in ground holding are covered in some detail. We conclude the review with suggestions on how singular perturbation theory could play a role in analyzing disruptions to such highly sensitive schedules as those in the civil aviation industry.     

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.     

A set packing model for the ground holding problem in congested networks

Air traffic flow management (ATFM) consists of several activities performed by control authorities in order to reduce delays due to traffic congestion. Ground holding decisions restrict certain flights from tacking off at the scheduled departure time if congestion is expected at the destination airport. They are motivated by the fact that it is safer to hold an aircraft on the ground than in the air. Several integer linear programming models have been proposed to efficiently solve the ground holding problem (GHP). In this paper we investigate a set packing formulation of the GHP and design a branch-and-cut algorithm to solve the problem in high congestion scenarios, i.e., when lack of capacity induces flights cancellation. The constraint generation is carried out by heuristically solving the separation problem associated with a large class of rank inequalities. This procedure exploits the special structure of the GHP's intersection graphs. The computational results indicate that the proposed algorithm outperforms other algorithms in which flight cancellation has been allowed.     

Flight gate scheduling with respect to a reference schedule

This paper considers the problem of assigning flights to airport gates. We examine the general case in which an aircraft serving a flight may be assigned to different gates for arrival and departure processing and for optional intermediate parking. Restrictions to this assignment include gate closures and shadow restrictions, i.e., the situation where certain gate assignments may cause blocking of neighboring gates. The objectives include maximization of the total assignment preference score, a minimal number of unassigned flights during overload periods, minimization of the number of tows, maximization of a robustness measure as well as a minimal deviation from a given reference schedule. We show that in case of a one period time horizon this objective can easily be integrated into our existing model based on the Clique Partitioning Problem. Furthermore we present a heuristic algorithm to solve the problem for multiple periods.     

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.     

Digital Simulations of Runway Utilization

Queues of aircraft that form at airports, both in the air and on the ground, are the biggest source of delay in civil air transport operations. The study of these queues is complicated by the fact that the times at which aircraft join the queues are not independent, and also by considerable diurnal fluctuation of traffic.This paper describes an approach, primarily through simulation of idealized models, on a digital computer. The object of the work was to obtain insight into the behaviour of runway queues rather than to imitate the activity of a particular airport. The models used assume that the arrival times at the queues are the result of a scheduled pattern being disordered through aircraft being independently early or late. Such an arrival process degenerates to a Poisson process if the discrepancies from schedule are very large, but in practice it is significantly different. Results from 300,000 simulated take-offs and landings are given.     

空中交通流量管理中的改航策略研究

针对在恶劣天气下出现的大规模航班延误情况,根据机场和航路段的动态容量约束,建立了改航策略模型,并提出求解该模型的有效算法.选择全国航班时刻表进行仿真,仿真结果表明:该模型提供了在恶劣天气下更安全、更经济的航班改航策略,可为战术级流量管理提供辅助决策.     

基于优先级的进离港航班排序优化问题研究

研究机场终端区进离港航班排序优化问题,对于提高跑道利用率以及降低航班延误损失具有重要意义。本文首先考虑航班运行方式(降落和起飞)、飞机类型以及航班的重要程度(航程是否连续)的不同所造成延误损失的不同,设计三维优先级表反映调度优先等级,并将其转化为延误成本系数。其次,为实现调度的公平性和减轻管制人员的工作负荷,设置允许延误的航班架次约束、邻边约束以及最大限制位置约束。再次,以最小化航班总延误成本为目标建立模型,提出相应的改进蚁群算法(GJAC)进行求解。最后通过数值实验验证所提算法在考虑调度优先等级及上述约束条件的同时能有效减少进离港航班队列的总延误成本。     

Models for single-sector stochastic air traffic flow management under reduced airspace capacity

Air traffic efficiency is heavily influenced by unanticipated factors that result in capacity reduction. Of these factors, weather is the most significant cause of delays in airport and airspace operations. Considering weather-related uncertainty, air traffic flow management involves controlling air traffic through allocation of available airspace capacity to flights. The corresponding decision process results in a stochastic dynamic problem where aircraft on the ground and in the air are controlled based on the evolution of weather uncertainty. We focus on the single-sector version of the problem that is applicable to a majority of cases where a volume of airspace has reduced capacity due to convective weather. We model the decision process through stochastic integer programming formulations and computationally analyse it for tractability. We then demonstrate through actual flight schedule data that a simplistic but practically implementable approximation procedure is a generally effective solution approach for these models.     

Minimizing total weighted late work in the resource-constrained project scheduling problem

This paper deals with resource-constrained project scheduling problem under the weighted late work criterion. Late work objective functions estimate the quality of a schedule based on durations of late parts of activities, not taking into account the amount of delay for fully late activities. It is assume that a project contains activities interrelated by finish-to-start type precedence relations with time lag of zero, which require one or more constrained renewable resources. The objective is to schedule each activity such that the total weighted late work is minimized. The problem has been formulated using a linear integer programming model and solved by the CPLEX. Also, a set of priority rules have been designed to quickly generate a set of initial solutions. In order to solve the problem optimally, a depth-first branch-and-bound algorithm is applied based on idea of minimal delaying alternatives. The branching order of nodes that belong to the same level of the search tree is determined on the basis of the developed priority rules. This results in generation six different versions of the branch-and-bound algorithm. Computational results on randomly generated problem sets are provided to analyze the efficiency of the priority rules and the branch-and-bound algorithm.     

基于分支割平面的一类无容量限制设施选址问题求解算法

无容量限制设施选址问题是经典的组合优化问题, 具有广泛的应用价值,然而该问题已被证明是NP难问题, 并且传统的分支定界方法求解速度较慢.研究以最大化总收益费用与总投建费用之差为目标的无容量限制设施选址问题,将其转化为节点包装问题,并根据模型的图形特点提出了新的合法不等式族------轴不等式族,经过严格的数学证明后得出轴不等式要强于原有的奇洞不等式. 同时,设计出切割不等式快速搜索算法嵌入到分支割平面方法中. 最后,通过实验验证了轴不等式族的强有效性, 以及分支割平面方法比分支定界方法求解速度快、节点数量少的优点.     

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.     

A gate reassignment framework for real time flight delays

Flight delays (such as early or late arrivals and late departures) are a frequent occurrence in actual day to day airport operations and it is often not possible to assign such flights to their original gates. Flight delay information may also vary with time. As a consequence, the airport authority needs to reassign flights to different gates in real-time. The traditional manual flight reassignment method is neither efficient nor effective in cases with variable flight delay information, and the reassignment is frequently time constrained. Consequently, in this study the goal is to develop a gate reassignment framework, and a systematic computerized tool, for repeatedly handling gate reassignments given varied flight delay information. The results of a test case related to Taiwan international airport operations, show that the proposed framework performs well.     

A compact optimization model for the tail assignment problem

This paper investigates a new model for the so-called Tail Assignment Problem, which consists in assigning a well-identified airplane to each flight leg of a given flight schedule, in order to minimize total cost (cost of operating the flights and possible maintenance costs) while complying with a number of operational constraints. The mathematical programming formulation proposed is compact (i.e., involves a number of $0?1$ decision variables and constraints polynomial in the problem size parameters) and is shown to be of significantly reduced dimension as compared with previously known compact models. Computational experiments on series of realistic problem instances (obtained by random sampling from real-world data set) are reported. It is shown that with the proposed model, current state-of-the art MIP solvers can efficiently solve to exact optimality large instances representing 30-day flight schedules with typically up to 40 airplanes and 1500 flight legs connecting as many as 21 airports. The model also includes the main existing types of maintenance constraints, and extensive computational experiments are reported on problem instances of size typical of practical applications.     

Robust berth scheduling with uncertain vessel delay and handling time

In container terminals, the actual arrival time and handling time of a vessel often deviate from the scheduled ones. Being the input to yard space allocation and crane planning, berth allocation is one of the most important activities in container terminals. Any change of berth plan may lead to significant changes of other operations, deteriorating the reliability and efficiency of terminal operations. In this paper, we study a robust berth allocation problem (RBAP) which explicitly considers the uncertainty of vessel arrival delay and handling time. Time buffers are inserted between the vessels occupying the same berthing location to give room for uncertain delays. Using total departure delay of vessels as the service measure and the length of buffer time as the robustness measure, we formulate RBAP to balance the service level and plan robustness. Based on the properties of the optimal solution, we develop a robust berth scheduling algorithm (RBSA) that integrates simulated annealing and branch-and-bound algorithm. To evaluate our model and algorithm design, we conduct computational study to show the effectiveness of the proposed RBSA algorithm, and use simulation to validate the robustness and service level of the RBAP formulation.     

航空公司中的飞行员配置研究

随着新航线的开辟和新飞机的投入使用,航空公司的任务量急剧增长,飞行员需求的估计和机组的合理配置变得日益重要。本文基于实际工作需求,提出一类用于评估飞行员数量,并进行机组均衡配置的整数规划模型,为航空公司进行飞行员的数量评估和任务分配提供决策支持。本文在以下两个方面做出改进:1)加入国际长途航线,研究国内短途航线和国际长途航线混合搭配情况下飞行员的配置问题;2)鉴于大型整数规划求解的复杂性,通过评估航空公司所需要的飞行员数量的下界,为决策人员制定中长期规划提供依据。本文通过启发式算法进行飞行员的配置,计算结果接近理论问题的下界,证明了算法的有效性。     

Optimal dispatching strategy on an airline network after a schedule perturbation

It often happens that one or more aeroplanes from an airline fleet are taken out of operation for technical reasons and the airline has to operate on the existing network with a reduced number of planes. This paper presents the results of an effort to define a new ad hoc schedule for this situation, so that the total passenger delay on an airline network is minimized. A network is formed, in which nodes represent flights on a given airline network, and arcs are the total time losses on individual flights. The problem of determining a new routing and scheduling plan for the airline fleet is solved by branch and-bound methods. A numerical example illustrates the efficiency of the model.     

枢纽机场终端区PBN模式下最优跑道数需求

针对我国枢纽机场日起降高峰小时的航班拥堵常态化问题,从系统整体运行效能的角度,针对枢纽机场终端区跑道系统容量瓶颈,①分析性能基导航(Perormance-Based Navigation,PBN)模式下枢纽机场终端区的空域结构、飞行、管制程序,根据随机服务系统理论,建立其运行模型;②考虑PBN模式下航班、旅客的延误滞留函数和机场单位时间服务支出函数;③再应用排队论和系统运行效能理论,建立枢纽机场最佳跑道数目需求算法,能根据相关参数计算航班滞留时间和队长等指标;④最后引用某枢纽机场相关数据,演算结果符合实际抽样调查统计资料.     

A dynamic programming approach for the airport capacity allocation problem

In most of the optimization models developed to manage airportsoperations, arrivals and departures capacities are treated asindependent variables: that is the number of flights allowedto take off does not affect the number of landings in any unitof time, and vice versa. This assumption is seldom verifiedin most of the congested airports, where many interactions betweenarrivals and departures take place. In this paper, we face the problem of finding the optimal trade-offbetween the number of arrivals and departures in order to reducea delay function of all the flights, using a more realisticrepresentation of the airport capacity, i.e. the capacity envelope. Under the assumption of piecewise linear convex capacity envelopesand of the exact interpolation of all the Pareto-optimal operationalpoints, we show that the problem can be formulated as a linearprogramming model. For general airport capacity envelopes, wepropose a dynamic programming formulation with a correspondingbackward solution algorithm, which is robust, easy to implementand has a linear computational complexity. The algorithm performancesare evaluated on different realistic scenarios, and the optimalsolutions are compared with those computed by a greedy algorithm,which can be seen as an approximation of the current decisionprocedures. The percentage deviation of the cost of these twosolutions ranges from 3.98 to 35.64%.