A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding

We consider a monthly crew scheduling problem with preferential bidding in the airline industry. We propose a new methodology based on a graph coloring model and a tabu search algorithm for determining if the problem contains at least one feasible solution. We then show how to combine the proposed approach with a heuristic sequential scheduling method that uses column generation and branch-and-bound techniques.     

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.     

An integrated scenario-based approach for robust aircraft routing,crew pairing and re-timing

For reasons of tractability, the airline scheduling problem has traditionally been sequentially decomposed into various stages (e.g. schedule generation, fleet assignment, aircraft routing, and crew pairing), with the decisions from one stage imposed upon the decision-making process in subsequent stages. Whilst this approach greatly simplifies the solution process, it unfortunately fails to capture many dependencies between the various stages, most notably between those of aircraft routing and crew pairing, and how these dependencies affect the propagation of delays through the flight network. In Dunbar et al. (2012) [9] we introduced a new algorithm to accurately calculate and minimize the cost of propagated delay, in a framework that integrates aircraft routing and crew pairing. In this paper we extend the approach of Dunbar et al. (2012) [9] by proposing two new algorithms that achieve further improvements in delay propagation reduction via the incorporation of stochastic delay information. We additionally propose a heuristic, used in conjunction with these two approaches, capable of re-timing an incumbent aircraft and crew schedule to further minimize the cost of delay propagation. These algorithms provide promising results when applied to a real-world airline network and motivate our final integrated aircraft routing, crew pairing and re-timing approach which provides a substantially significant reduction in delay propagation.     

Review of real-time vehicle schedule recovery methods in transportation services

This paper presents a comprehensive review on methods for real-time schedule recovery in transportation services. The survey concentrates on published research on recovery of planned schedules in the occurrence of one or several severe disruptions such as vehicle breakdowns, accidents, and delays. Only vehicle assignment and rescheduling are reviewed; crew scheduling and passenger logistics problems during disruptions are not. Real-time vehicle schedule recovery problems (RTVSRP) are classified into three classes: vehicle rescheduling, for road-based services, train-based rescheduling, and airline schedule recovery problems. For each class, a classification of the models is presented based on problem formulations and solution strategies. The paper concludes that RTVSRP is a challenging problem that requires quick and good quality solutions to very difficult and complex situations, involving several different contexts, restrictions, and objectives. The paper also identifies research gaps to be investigated in the future, stimulating research in this area.     

A network-based approach to the multi-activity combined timetabling and crew scheduling problem: Workforce scheduling for public health policy implementation

This paper introduces the multi-activity combined timetabling and crew scheduling problem. The goal of this problem is to schedule the minimum number of workers required in order to successfully visit a set of customers characterized by services needed matched against schedule availability. Two solution strategies are proposed. The first is based on mathematical programming whilst the second uses a heuristic procedure in order to reduce computational time. The proposed model combines timetabling with crew scheduling decisions in one mixed integer programming model which considers multiple activities. The algorithms are tested on randomly generated and real instances provided by the Health to School Initiative, a program based at Bogotá’s local Health Department. The results show that the Initiative can increase its coverage by up to 68% using the proposed heuristic approach as a planning process tool.     

An integer programming approach to generating airline crew pairings

The ability to generate crew pairings quickly is essential to solving the airline crew scheduling problem. Although techniques for doing so are well-established, they are also highly customized and require significant implementation efforts. This greatly impedes researchers studying important problems such as robust planning, integrated planning, and automated recovery, all of which also require the generating of crew pairings. As an alternative, we present an integer programming (IP) approach to generating crew pairings, which can be solved via traditional methods such as branch-and-bound using off-the-shelf commercial solvers. This greatly facilitates the prototyping and testing of new research ideas. In addition, we suggest that our modeling approach, which uses both connection variables and marker variables to capture the non-linear cost function and constraints of the crew scheduling problem, can be applicable in other scheduling contexts as well. Computational results using data from a major US hub-and-spoke carrier demonstrate the performance of our approach.     

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.     

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.     

Aircraft maintenance,routing, and crew scheduling planning for airlines with a single fleet and a single maintenance and crew base

This work proposes an approach for solving the aircraft maintenance routing problem (AMRP) and the crew scheduling problem (CSP) in sequential and integrated fashions for airlines having a single fleet with a single maintenance and crew base, as is the case for most Latin American and many low-cost airlines. The problems were initially solved in the traditional sequential fashion. The AMRP was formulated to maximize revenue while satisfying fleet size. It was solved such that the final flight schedule was also determined. The CSP was solved by including a heuristic to obtain an efficient first feasible solution, and adapting a labeling algorithm to solve the pricing problems that arise in the column-generation technique. Finally, an integrated model was formulated and solved. Both approaches were tested on the real flight schedules of three important Latin American airlines. The solutions were coherent, independent of computational parameters, and obtained in short computational times in a standard PC (e.g. <1 h for up to 522 flights). Continuous relaxations gave very tight bounds (e.g. gaps < 0.8%). The integrated solutions offered small improvements over the sequential solutions (e.g. up to 0.6% or US$45,000 savings/year). However, these savings should increase drastically with fleet size and with the complexity of the flight schedule offered by the airline.     

Crew pairing optimization based on hybrid approaches

The crew pairing problem (CPP) deals with generating crew pairings due to law and restrictions and selecting a set of crew pairings with minimal cost that covers all the flight legs. In this study, we present three different algorithms to solve CPP. The knowledge based random algorithm (KBRA) and the hybrid algorithm (HA) both combine heuristics and exact methods. While KBRA generates a reduced solution space by using the knowledge received from the past, HA starts to generate a reduced search space including high quality legal pairings by using some mechanisms in components of genetic algorithm (GA). Zero-one integer programming model of the set covering problem (SCP) which is an NP-hard problem is then used to select the minimal cost pairings among solutions in the reduced search space. Column generation (CG) which is the most commonly used technique in the CPP literature is used as the third solution technique. While the master problem is formulated as SCP, legal pairings are generated in the pricing problem by solving a shortest path problem on a structured network. In addition, the performance of CG integrated by KBRA (CG_KBRA) and HA (CG_HA) is investigated on randomly generated test problems. Computational results show that HA and CG_HA can be considered as effective and efficient solution algorithms for solving CPP in terms of the computational cost and solution quality.     

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.     

基于SMT的机组排班问题优化求解

机组排班是航空公司运营计划非常重要的一个环节,合理的机组排班可以为航空公司省下一大笔机组成本支出,从而增加航空公司的收益.由于机组排班过程涉及大量的复杂约束,属于NP难问题,因此优化求解困难.本文提出了一种基于可满足性模理论(Satisfiability Modulo Theories,SMT)的航空公司机组排班问题的优化求解方法,将机组排班过程中的各种约束转化为一阶逻辑公式,设立求解目标为最小化成本和最大化机组利用率,将问题转化为求在给定逻辑公式可满足情况下的最优解,并利用SMT求解器Z3进行求解.实验表明,本文的算法能有效的求解一定规模航班计划的机组排班问题,给航空公司带来一定的收益.     

Genetic algorithms for match-up rescheduling of the flexible manufacturing systems

Scheduling plays a vital role in ensuring the effectiveness of the production control of a flexible manufacturing system (FMS). The scheduling problem in FMS is considered to be dynamic in its nature as new orders may arrive every day. The new orders need to be integrated with the existing production schedule immediately without disturbing the performance and the stability of existing schedule. Most FMS scheduling methods reported in the literature address the static FMS scheduling problems. In this paper, rescheduling methods based on genetic algorithms are described to address arrivals of new orders. This study proposes genetic algorithms for match-up rescheduling with non-reshuffle and reshuffle strategies which accommodate new orders by manipulating the available idle times on machines and by resequencing operations, respectively. The basic idea of the match-up approach is to modify only a part of the initial schedule and to develop genetic algorithms (GAs) to generate a solution within the rescheduling horizon in such a way that both the stability and performance of the shop floor are kept. The proposed non-reshuffle and reshuffle strategies have been evaluated and the results have been compared with the total-rescheduling method.     

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Petri网的批处理调度研究

批处理过程存在于复杂的动态环境中,来自主客观的干扰及问题固有的易变性,会导致各种过程参数的变化,因此,需要研究对意外事件作出快速反应的动态调度方法,以捕捉生产环境的实时变化。该文针对批处理过程中最常出现的操作处理时间波动,提出了基于Petri网仿真技术的批处理过程动态调度方法。仿真结果表明,该方法能有效地改善调度性能,为批处理过程动态调度的研究提供了新思路。     

基于人机交互的炼钢连铸动态调度*

针对炼钢连铸动态调度问题,建立了问题的优化模型、设计了约束满足求解算法并分析了算法复杂度、开发了炼钢连铸动态调度的人机交互系统。当生产过程中的扰动事件发生时,系统能够通过人机交互并结合优化模型和多项式时间复杂度的算法获得可行且与原调度尽量一致的新调度方案,以确保动态调度前后整个生产过程的连续性和稳定性。     

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.     

分布式整数规划及其在航线扰动问题的应用

在航空公司的运作中时常会出现干扰它正常运作的现象。在这种情况下,航空公司必须马上制定航线修复计划使受到干扰的航线尽快复原,以防止更大面积的航班取消和航班延误。提出一种基于递增映射迭代方法的分布式整数规划算法来解决由于机场关闭引起的航线扰动问题。整个问题分成了两个子问题：可行航线的生成和飞机的重指派。第一个子问题的问题空间被初始点分割方法分割成了若干片段。然后在一个分布式的计算网络中使用递增映射迭代方法在分得的每个片段上同时求解第一个子问题。得到的可行航线用来求解第二个子问题。最后的算例结果可以发现提出的方法要好于CPLEX和多目标基因算法。     

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.     

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.