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.     

A hybrid meta-heuristic algorithm for optimization of crew scheduling

Crew scheduling problem is the problem of assigning crew members to the flights so that total cost is minimized while regulatory and legal restrictions are satisfied. The crew scheduling is an NP-hard constrained combinatorial optimization problem and hence, it cannot be exactly solved in a reasonable computational time. This paper presents a particle swarm optimization (PSO) algorithm synchronized with a local search heuristic for solving the crew scheduling problem. Recent studies use genetic algorithm (GA) or ant colony optimization (ACO) to solve large scale crew scheduling problems. Furthermore, two other hybrid algorithms based on GA and ACO algorithms have been developed to solve the problem. Computational results show the effectiveness and superiority of the proposed hybrid PSO algorithm over other algorithms.     

Knowledge based-system for alternative design,cost estimating and scheduling

The traditional design, cost estimating and scheduling procedures focus on assessing costs and schedule after design decisions are made and conveyed to construction drawings and design that is, they do not have a mechanism that allow the designer to perform a rapid ‘what if’ analysis on design alternatives and cost analysis of different types of building materials and alternative schedule analysis at early stage of project without accompanying of detailed design and drawing. Moreover, the available scheduling tools are not integrated to design and cost estimating system and hence require manual input of activities lists, activities sequencing, resources, costs and durations to generate project schedule and they are unable to consider the effect of productivity factors and the resulting uncertainty inherent in each activity. This paper presents an integrated knowledge based system for construction cost estimating and scheduling. The knowledge based system supports an automated alternative design analysis with on line schematic drawing, material selection, crew selection and productivity analysis for generating activities sequencing, normal durations, productivity adjusted durations, cost estimate, list of materials selected and their respective quantities and list of assigned crew. An analysis of alternative design, cost estimating and scheduling for a residential building using the integrated system is presented.     

A new heuristic branching scheme for the crew pairing problem with base constraints

Airline crew scheduling is typically performed in two steps : crew pairing followed by crew assignment. The crew pairing problem (CPP) finds a set of pairings (sequences of flights separated by connections or rests starting and ending at the same crew base) that covers a set of flights at minimum cost. The crew assignment problem consists of assigning the crew members to these pairings to create their individual schedules. The main downside of this sequential approach is that the pairings generated in the first step are not all suitable for the crew assignment step, yielding poor-quality solutions. This paper studies an extension of the CPP that includes additional constraints limiting the total worked time at each crew base. This problem, called the CPP with base constraints (CPPBC), is designed to improve the coupling of the two scheduling steps. To solve the CPPBC, we develop four branch-and-price heuristics: three of them rely on known heuristic branching schemes, the other introduces a new branching method, called retrospective branching. This branching scheme is designed to detect and revise poor branching decisions made earlier in the search tree, without backtracking. We tested and compared these four heuristics on real-world datasets. Our results show that the algorithm with retrospective branching yields, most of the times, better-quality solutions than the other tested methods.     

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.     

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.     

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.     

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.     

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.     

Cooperative power-aware scheduling in grid computing environments

Energy usage and its associated costs have taken on a new level of significance in recent years. Globally, energy costs that include the cooling of server rooms are now comparable to hardware costs, and these costs are on the increase with the rising cost of energy. As a result, there are efforts worldwide to design more efficient scheduling algorithms. Such scheduling algorithm for grids is further complicated by the fact that the different sites in a grid system are likely to have different ownerships. As such, it is not enough to simply minimize the total energy usage in the grid; instead one needs to simultaneously minimize energy usage between all the different providers in the grid. Apart from the multitude of ownerships of the different sites, a grid differs from traditional high performance computing systems in the heterogeneity of the computing nodes as well as the communication links that connect the different nodes together. In this paper, we propose a cooperative, power-aware game theoretic solution to the job scheduling problem in grids. We discuss our cooperative game model and present the structure of the Nash Bargaining Solution. Our proposed scheduling scheme maintains a specified Quality of Service (QoS) level and minimizes energy usage between all the providers simultaneously; energy usage is kept at a level that is sufficient to maintain the desired QoS level. Further, the proposed algorithm is fair to all users, and has robust performance against inaccuracies in performance prediction information.     

考虑泊位偏好和岸桥移动的泊位岸桥联合调度

为了更高效地利用码头资源,同时考虑泊位资源和岸桥资源,建立了考虑泊位偏好和岸桥移动频数的泊位岸桥联合调度两阶段模型.第一阶段模型采用船舶到港时间可变的到港策略,建立了以船舶等待成本、泊位偏离成本、延迟离港成本之和最小为目标的混合整数规划模型.第二阶段模型考虑了岸桥的干扰约束,建立了以岸桥移动频数最小为目标的整数规划模型...     

呼叫中心排班优化模型的研究

呼叫中心排班系统的优化研究是在话务员和坐席资源约束下,根据服务需求时间序列,合理安排资源,以提高呼叫接入服务质量、提高话务员的个性化满意度和降低运营成本的多目标复杂约束的优化问题。根据客服质量与话务员满意度相关的指标和约束,引入了服务水平、排班成本、话务员疲劳度、排班公平性和话务员意愿等因素。基于对满足服务水平的班组数量的预测,依据对外的规划经营和对内的管理调度的区别,将排班决策分为班次设计和班组指派两大具有递进关系的子模型。利用改进型PSO算法和旋转排班法进行求解,并且根据排班结果和评价参数对规划调度参数进行反馈调整。最后通过仿真分析说明了本文方法在兼顾客服满意度和话务员满意度的呼叫中心排班决策系统中有很好的适应性。     

Generation maintenance scheduling in power systems using ant colony optimization for continuous domains based 0–1 integer programming

In this paper, we present a formulation that enables Ant Colony Optimization for Continuous Domains (ACO_R) to seek the optimal solution of the unit maintenance scheduling problem. ACO_R is a direct extension of Ant Colony Optimization (ACO). Also it is the significant ant-based algorithm for continuous optimization. For the maintenance scheduling, cost reduction is as important as reliability. The objective function of this algorithm considers the effect of economy as well as reliability. Various constraints such as spinning reserve, duration of maintenance crew are being taken into account. The ACO_R formulation developed is applied on a power system with six generating units. The simulation result of this technique is compared with those reported in literature. The outcome is very encouraging and proves that the authors’ proposed approach outperforms them in terms of reaching a better optimal solution and speed.     

Operational airline reserve crew planning

Airlines are continually faced with the challenge of efficient utilization of their cockpit crew resources. In addition to regular flying crews, some airlines have to maintain significant reserve staffing levels to meet contractual obligations and provide smooth daily operations. Reserve crews are required to cover trips remaining unassigned due to disruptions during daily operations. Airlines using a bidline system to award crew work schedules require additional reserves to cover scheduling conflicts, which result in trips dropping out of optimized bidlines. Whenever reserves are unavailable to cover these trips during daily operations, the airline has to pay a premium to cover these trips using regular pilots. The resulting operating expenses can be significant. Furthermore, inefficient utilization of reserves can cause excessive long-range crew staffing resulting in additional training and new hire expenses. In this paper, we propose a new optimization strategy to increase reserve crew utilization and build monthly reserve crew work schedules by addressing the issue of scheduling conflicts and daily operational reserve requirements.     

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.     

A knowledge-based decision support system for shipboard damage control

The operational complexity of modern ships requires the use of advanced applications, called damage control systems (DCSs), able to assist crew members in the effective handling of dangerous events and accidents. In this article we describe the development of a knowledge-based decision support system (KDSS) integrated within a DCS designed for a national navy. The KDSS uses a hybrid design and runtime knowledge model to assist damage control operators through a kill card function which supports damage identification, action scheduling and system reconfiguration. We report a fire fighting scenario as illustrative application and discuss a preliminary evaluation of benefits allowed by the system in terms of critical performance measures. Our work can support further research aimed to apply expert systems to improve shipboard security and suggest similar applications in other contexts where situational awareness and damage management are crucial.     

基于蚁群算法的泊位调度问题

在集装箱港口的运作中,泊位调试系统是制约集装箱港口降低船舶在港时间和运营成本的主要瓶颈之一。泊位调度的目标就是确定集装箱港口船舶的停靠泊位和停泊时间。将码头看成离散泊位的集合,以船舶的在港时间最短为目标,应用蚁群算法对该问题进行优经研究,在满足各种约束条件的基础上,充分的利用好码头资源。利用蚁群算法的正反馈和并行搜索特点提高解的质量2和稳定性,通过对某集装箱码头的案例分析,说明该算法的有效性和实用性。     

Integrated aircraft-path assignment and robust schedule design with cruise speed control

Assignment of aircraft types, each having different seat capacity, operational expenses and availabilities, critically affects airlines’ overall cost. In this paper, we assign fleet types to paths by considering not only flight timing and passenger demand, as commonly done in the literature, but also operational expenses, such as fuel burn and carbon emission costs associated with adjusting the cruise speed to ensure the passenger connections. In response to flight time uncertainty due to the airport congestions, we allow minor adjustments on the flight departure times in addition to cruise speed control, thereby satisfying the passenger connections at a desired service level. We model the uncertainty in flight duration via a random variable arising in chance constraints to ensure the passenger connections. Nonlinear fuel and carbon emission cost functions, chance constraints and binary aircraft assignment decisions make the problem significantly more difficult. To handle them, we use mixed-integer second order cone programming. We compare the performance of a schedule generated by the proposed model to the published schedule for a major U.S. airline. On the average, there exists a 20% overall operational cost saving compared to the published schedule. To solve the large scale problems in a reasonable time, we also develop a two-stage algorithm, which decomposes the problem into planning stages such as aircraft-path assignment and robust schedule generation, and then solves them sequentially.     

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.