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Integrated cruise fleet deployment and itinerary scheduling problem: An enhanced Benders decomposition approach 综合邮轮舰队部署和行程安排问题:一种增强的Benders分解方法
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-29 DOI: 10.1016/j.trb.2025.103321
Ying Yang, Silong Zhang, Shuaian Wang
With the growing popularity of cruise tourism, the issue of comprehensive and precise cruise management is emphasized by the industrial field, which demands effective strategies in both tactical-level cruise deployment and operational-level itinerary scheduling. This rising concern and the expectation of integrated decision, however, increase the complexity of the problem and the difficulty of optimization. This paper provides a cohesive framework and scalable algorithms for the integrated cruise fleet deployment and itinerary scheduling problem. First, to address this problem, we propose an integer programming model based on a time-expanded network that captures the movement dynamics of cruises over a planning horizon. Several problem-specific reformulations including cumulative-flow-based variables and route-based time-expanded network representation are introduced, based on which, we prove that the itinerary scheduling problem is totally unimodular and the integer variables can be relaxed. Second, we introduce a tailored Benders decomposition approach augmented by the simultaneous Magnanti–Wong method, where a valid and pre-obtainable Magnanti–Wong bound is designed, yielding Pareto-optimal cuts in small computation time in each iteration. Finally, we validate our approach using extensive numerical experiments on both simulation instances and a real case study. The results demonstrate the effectiveness of our integrated solving scheme and the practical applicability of our advanced decomposition method, marking a significant advancement in the field of cruise fleet management.
随着邮轮旅游的日益普及,邮轮的全面、精准管理问题越来越受到工业界的重视,这就要求在战术层面的邮轮部署和运营层面的行程安排上都有有效的策略。然而,这种日益增长的关注和对综合决策的期望,增加了问题的复杂性和优化的难度。本文为邮轮编队部署和行程调度问题提供了一个内聚框架和可扩展算法。首先,为了解决这个问题,我们提出了一个基于时间扩展网络的整数规划模型,该模型可以在规划范围内捕获巡航的运动动态。引入了基于累积流的变量和基于路线的时间扩展网络表示,证明了行程调度问题是完全非模的,整数变量可以松弛。其次,我们引入了一种定制的Benders分解方法,该方法由同时的Magnanti-Wong方法扩展,其中设计了一个有效且可预获得的Magnanti-Wong界,在每次迭代中以较小的计算时间产生pareto最优切割。最后,我们在模拟实例和实际案例研究中使用广泛的数值实验来验证我们的方法。结果表明了综合求解方案的有效性和先进分解方法的实用性,在邮轮船队管理领域取得了重大进展。
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引用次数: 0
A scalable optimization approach for equitable facility location: Methodology and transportation applications 一个可扩展的优化方法为公平的设施选址:方法和运输应用
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-29 DOI: 10.1016/j.trb.2025.103319
Drew Horton , Joshua Murrell , Daphne Skipper , Emily Speakman , Tom Logan
Efficient and equitable access to essential services, such as healthcare, food, and education, is an important goal in urban planning, public policy, and transport logistics. However, existing facility location models often do not scale well to large instances, or primarily focus on optimizing average accessibility, neglecting equity concerns, particularly for disadvantaged populations. This paper proposes a novel, scalable framework for equitable facility location, introducing a linearized proxy for the Kolm-Pollak Equally-Distributed Equivalent (EDE) metric to balance efficiency and fairness. Computational experiments demonstrate that our approach scales to extremely large problem instances, while being sensitive enough to account for inequity throughout the distribution, not merely via the maximum value. Moreover, optimal solutions represent significant improvements for the worst-off residents in terms of distance to an open amenity, while also attaining a near-optimal average experience for all users. An extensive real-world case study on supermarket access illustrates the practical applicability of the framework, with additional examples coming from polling applications. As such, the model is extended to handle real-world considerations such as capacity constraints, split demand assignments, and location-specific penalties. By bridging the gap between equity theory and practical optimization, this work offers a robust and versatile tool for researchers and practitioners in urban planning, transportation, and public policy.
有效和公平地获得医疗保健、食品和教育等基本服务是城市规划、公共政策和运输物流的一个重要目标。然而,现有的设施选址模型往往不能很好地扩展到大型实例,或者主要侧重于优化平均可达性,而忽略了公平问题,特别是对弱势群体。本文提出了一种新的、可扩展的公平设施选址框架,引入了Kolm-Pollak等分布当量(EDE)度量的线性化代理,以平衡效率和公平性。计算实验表明,我们的方法适用于非常大的问题实例,同时足够敏感,可以解释整个分布的不平等,而不仅仅是通过最大值。此外,最优解决方案对于最贫困的居民来说,在与开放设施的距离方面有显著改善,同时也为所有用户实现了接近最佳的平均体验。一个关于超市访问的广泛的实际案例研究说明了该框架的实际适用性,还有来自轮询应用程序的其他示例。因此,该模型被扩展为处理现实世界的考虑因素,例如容量限制、需求分配和特定位置的惩罚。通过弥合公平理论与实践优化之间的差距,这项工作为城市规划、交通和公共政策的研究人员和实践者提供了一个强大而通用的工具。
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引用次数: 0
Toward mobility incentive: Integrating green service and carbon inclusion scheme into the ride-hailing market 出行激励:将绿色服务和碳排放纳入网约车市场
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-24 DOI: 10.1016/j.trb.2025.103320
Wei Tang , Xiqun (Michael) Chen , Der-Horng Lee
Increasing individual responsibility for reducing emissions is a potentially effective way to address mobility sustainability issues. In recent years, the carbon inclusion scheme has been widely implemented to incentivize individual low-carbon travel behaviors. Motivated by the practice, this paper examines the ride-hailing market that integrates the green service with the carbon inclusion scheme to comprehend how the government-led carbon inclusion scheme affects the operation of the ride-hailing market and the prospects of reducing carbon emissions and promoting electrification. We propose two product strategies for the ride-hailing platform: (a) One-product strategy with mixed service provided by electric vehicles (EVs) and fuel vehicles (FVs); and (b) Differentiated-product strategy with green service provided by EVs and basic service provided by FVs. We also consider the significant differences in adopting electric buses in different countries/regions when discussing the impact of carbon inclusion on the ride-hailing market. Our findings indicate that without government-led carbon inclusion, it is more appropriate for the ride-hailing platform to adopt the one-product strategy. With government-led carbon inclusion, when the electrification rate of external public transportation is not very high, and the carbon incentive is high enough, the platform can improve its profit by adopting the differentiated-product strategy. Considering the platform's profit maximization decisions, our analysis also highlights that when the electrification rate of the external option is low and the carbon incentive is high, the impact of the carbon inclusion scheme on the ride-hailing market is better in all aspects, which is a win-win outcome that the ride-hailing platform, drivers, and the government would all like (if the government wants to see better driver welfare, electrification and carbon reduction in the ride-hailing market). Additionally, increasing the potential number of EVs in the ride-hailing market and the total number of drivers makes sense both for the platform (to gain higher profits) and government (which may be concerned about increasing driver welfare, the electrification rate and total carbon reduction of the ride-hailing market). The gained managerial insights provide decision support for the platform operating differentiated services and the government implementing carbon inclusion schemes.
增加个人在减排方面的责任是解决交通可持续性问题的潜在有效途径。近年来,碳包容计划被广泛实施,以激励个人的低碳出行行为。在实践的激励下,本文考察了绿色服务与碳包容计划相结合的网约车市场,了解政府主导的碳包容计划如何影响网约车市场的运行,以及减少碳排放和促进电气化的前景。我们为网约车平台提出了两种产品策略:(a)电动车和燃油车混合服务的单一产品策略;(b)电动汽车提供绿色服务和汽车提供基础服务的差异化产品战略。在讨论碳纳入对网约车市场的影响时,我们也考虑了不同国家/地区采用电动公交车的显著差异。我们的研究结果表明,如果没有政府主导的碳包容,网约车平台更适合采用单一产品策略。在政府主导的碳包容下,当外部公共交通的电气化率不是很高,而碳激励足够高时,平台可以通过采取差异化产品策略来提高其利润。考虑到平台的利润最大化决策,我们的分析还强调,当外部选项的电气化率较低而碳激励较高时,碳包容方案对网约车市场的影响在各个方面都更好,这是网约车平台、司机和政府都希望看到的双赢结果(如果政府希望看到更好的司机福利的话)。网约车市场的电气化和碳减排)。此外,增加网约车市场的潜在电动汽车数量和司机总数对平台(获得更高的利润)和政府(可能关心增加司机福利、电气化率和网约车市场的总碳减排)都是有意义的。获得的管理见解为平台运营差异化服务和政府实施碳包容计划提供决策支持。
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引用次数: 0
A modeling methodology for car-following behaviors of automated vehicles: Trade-off between stability and mobility 自动驾驶车辆跟车行为的建模方法:稳定性与机动性的权衡
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-16 DOI: 10.1016/j.trb.2025.103316
Yuqin Zhang , Ke Ma , Zhigang Xu , Hang Zhou , Chengyuan Ma , Xiaopeng Li
Empirical studies have indicated that automated vehicle (AV) automakers tend to prioritize mobility over stability in designing car-following (CF) models, which may raise safety concerns. A likely explanation for this issue is that hardware-induced response delays challenge the ability of the CF models, as designed by automakers, to maintain an equilibrium between stability and mobility. To address these concerns, this study proposes a modeling methodology for the CF model in AVs aimed at achieving a trade-off between stability and mobility. This methodology seeks to identify the optimal parameters that enhance mobility under stability constraints. First, the linear CF model is calibrated using data from 20 commercial AVs produced by multiple automakers, and the unique response delay values of the linear CF model for each AV are identified. Next, the parameter regions ensuring stability are derived theoretically based on the calibrated response delays for each AV. An optimal mobility objective function is constructed to minimize time headway and reaction time, with the boundaries of the stable parameter regions serving as constraints. It allows the selection of CF parameters that maximize mobility while remaining within the stable regions. This proposed modeling method is applied to all AVs, and the optimal parameters are tested in simulations. Simulation results demonstrate that the proposed optimal model effectively dampens oscillations, reduces safety risks, and maintains shorter spacing, thus achieving an ideal trade-off between stability and mobility for AVs.
实证研究表明,自动驾驶汽车(AV)制造商在设计汽车跟随(CF)模型时倾向于优先考虑移动性而不是稳定性,这可能会引发安全问题。对于这个问题,一个可能的解释是,硬件引起的响应延迟挑战了汽车制造商设计的CF模型在稳定性和移动性之间保持平衡的能力。为了解决这些问题,本研究提出了一种自动驾驶汽车CF模型的建模方法,旨在实现稳定性和移动性之间的权衡。该方法旨在确定在稳定性约束下增强机动性的最佳参数。首先,使用多家汽车制造商生产的20辆商用自动驾驶汽车的数据对线性CF模型进行校准,并确定每辆自动驾驶汽车的线性CF模型的唯一响应延迟值。其次,基于标定后的响应延迟,从理论上推导出保证稳定的参数区域,并以稳定参数区域的边界作为约束条件,构造出保证车头时距和反应时最小的最优机动性目标函数。它允许CF参数的选择,最大限度地提高流动性,同时保持在稳定区域内。将所提出的建模方法应用于所有自动驾驶汽车,并对最优参数进行了仿真验证。仿真结果表明,该优化模型有效地抑制了自动驾驶汽车的振荡,降低了安全风险,并保持了较短的间距,从而实现了自动驾驶汽车稳定性和移动性之间的理想平衡。
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引用次数: 0
Optimizing continuous-time berth allocation, time-variant quay crane and yard assignment 优化连续泊位分配、时变码头起重机和堆场分配
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-15 DOI: 10.1016/j.trb.2025.103317
Zhiyuan Yang , Miaomiao Wang , Shuaian Wang , Lu Zhen
Efficient container terminal operations depend on the coordinated use of three key resources: berths, quay cranes (QCs), and yard space. Decisions involving these components are highly interrelated. Berth allocation affects QC scheduling, which in turn influences yard-side transport. However, the majority of the literature treat these problems separately or under simplifying assumptions such as discrete berth allocation, time-invariant QC allocation, or omission of yard assignment. To the best of our known, this paper is the first to formulate a unified continuous-time optimization model that integrates continuous berth allocation, time-variant QC scheduling, and yard space assignment. To solve our proposed comprehensive decision model, we develop an exact algorithm and accelerate this by designing some novel valid inequalities and M-tightening techniques. The algorithmic efficiency and the benefits of considering the aforementioned decision features are validated through computational experiments. In addition, sensitivity analyses are conducted to derive potentially useful managerial insights.
高效的集装箱码头运营依赖于三个关键资源的协调使用:泊位、码头起重机(qc)和堆场空间。涉及这些组成部分的决策是高度相互关联的。泊位分配影响QC调度,进而影响场边运输。然而,大多数文献单独处理这些问题或简化假设,如离散泊位分配,定常QC分配,或遗漏码分配。据我们所知,本文首次建立了统一的连续时间优化模型,该模型集成了连续泊位分配、时变QC调度和堆场空间分配。为了解决我们提出的综合决策模型,我们开发了一个精确的算法,并通过设计一些新的有效不等式和m收紧技术来加速该算法。通过计算实验验证了算法的效率和考虑上述决策特征的好处。此外,还进行敏感性分析,以获得潜在有用的管理见解。
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引用次数: 0
Deep learning-based travel choice prediction with provable and adaptable fairness guarantees 基于深度学习的可证明和适应性公平性保证的出行选择预测
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-12 DOI: 10.1016/j.trb.2025.103318
Zhiwei Chen , Yufei Xu , Srinivas Peeta
Deep Learning (DL) models offer substantial potential for travel choice predictions but are often plagued by algorithmic unfairness where disadvantaged population groups such as racial minorities and low-income populations often receive disproportionately worse prediction outcomes (e.g. accuracy) compared to their counterparts. Studies to address this issue in the transportation domain are relatively new and they fail to provide provable fairness guarantees and cannot address the diverse interpretations of fairness in practice. This study introduces a novel DL approach that provides provable fairness guarantees while being adaptable to various fairness standards. It embeds statistical hypothesis testing within a practical equality constraint to control disparities in prediction accuracy across different population groups, thus providing provable and adaptable fairness guarantees. This approach results in a threshold modification problem, formulated as a mixed-integer non-linear programming model that is proven to be NP-hard. To allow for efficient problem solving, theoretical properties of the threshold modification problem are investigated, enabling the decomposition of the original problem into smaller, more manageable subproblems. This decomposition provides insights into the problem's structure and enables the development of an efficient "Accuracy-First-Threshold-Second " algorithmic framework. Within this framework, an exact solution method is proposed to achieve optimal solutions, whereas a heuristic method, incorporating a sandwich algorithm and a bounded-enumeration algorithm, is designed to efficiently approximate near-optimal solutions. Extensive experiments demonstrate the computational performance of the proposed solution algorithms as well as the ability of the proposed fair DL approach to provide provable and adaptable fairness guarantees for travel choice predictions. This study offers a flexible and theoretically robust solution to fairness in travel choice prediction, with potential applications for enhancing equity in transportation systems.
深度学习(DL)模型为旅行选择预测提供了巨大的潜力,但经常受到算法不公平的困扰,弱势群体,如少数民族和低收入人群,与同行相比,往往会得到不成比例的更差的预测结果(例如准确性)。在交通运输领域解决这一问题的研究相对较新,它们未能提供可证明的公平保证,也无法解决实践中对公平的各种解释。本研究提出了一种新的深度学习方法,该方法提供了可证明的公平保证,同时适应各种公平标准。它将统计假设检验嵌入到实际的平等约束中,以控制不同人群之间预测精度的差异,从而提供可证明和可适应的公平性保证。这种方法导致了一个阈值修改问题,它被表述为一个被证明是np困难的混合整数非线性规划模型。为了有效地解决问题,研究了阈值修改问题的理论性质,从而将原始问题分解为更小、更易于管理的子问题。这种分解提供了对问题结构的洞察,并使开发高效的“精度-第一-阈值-第二”算法框架成为可能。在此框架下,提出了精确解方法来获得最优解,而结合三明治算法和有界枚举算法的启发式方法来有效地逼近近最优解。大量的实验证明了所提出的解决算法的计算性能,以及所提出的公平深度学习方法为旅行选择预测提供可证明和可适应的公平性保证的能力。本研究为出行选择预测中的公平性问题提供了一个灵活且理论上稳健的解决方案,在提高交通系统公平性方面具有潜在的应用前景。
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引用次数: 0
Integrated optimization of train makeup problem and resource scheduling in railway marshalling yards: A hybrid MILP-CP approach with Logic-based Benders decomposition 铁路编组站列车编组问题与资源调度的综合优化:基于逻辑的Benders分解的混合MILP-CP方法
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-10 DOI: 10.1016/j.trb.2025.103306
Peiran Han , Lingyun Meng , Xiaojie Luan , Nikola Bešinović , Jianrui Miao , Yihui Wang , Zhengwen Liao
In the marshalling yard, various complex operations occur, leading to inefficiencies in railcar connections. Therefore, designing an effective operational research methodology is essential for the marshalling yard, and even for the local rail freight network. This paper addresses the integrated Train Makeup and Resource Scheduling (TMRS) problem. A Mixed-Integer Linear Programming (MILP) model is developed, where the train makeup problem is formulated as an assignment problem, guiding the overall operations. Additionally, a series of hybrid flow shop scheduling tasks are established to coordinate the operations of trains, blocks, and railcars. Due to the complexity of TMRS, the integrated problem is reformulated as a hybrid mixed-integer linear programming (MILP) and constraint programming (CP) model. Logic-based benders decomposition (LBBD) is used to partition the TMRS problem, with lower bounds designed and integrated into the solving procedure to accelerate the convergence. We propose feasibility cuts, optimality cuts, and symmetry cuts based on the structure of the subproblem, which are dynamically added to the master problem. Two numerical examples are designed to demonstrate the effectiveness of the proposed hybrid modelling approach, lower bounds, and cuts. Finally, the proposed approach and algorithm are tested on a series of artificial instances and real-scale examples, demonstrating their practical effectiveness and ability to achieve high-quality solutions.
在编组站,各种复杂的操作发生,导致铁路车辆连接效率低下。因此,设计一个有效的运筹学研究方法是必不可少的编组站,甚至为当地的铁路货运网络。本文研究了列车组成与资源调度的集成问题。建立了混合整数线性规划(MILP)模型,将列车组成问题转化为分配问题,指导整体运行。此外,还建立了一系列混合流车间调度任务,以协调列车、街区和轨道车辆的运行。考虑到TMRS问题的复杂性,将该问题重新表述为混合整数线性规划(MILP)和约束规划(CP)模型。采用基于逻辑的benders分解(LBBD)对TMRS问题进行划分,并在求解过程中设计下界,以加快收敛速度。提出了基于子问题结构的可行性切割、最优性切割和对称性切割,并将其动态添加到主问题中。设计了两个数值示例来证明所提出的混合建模方法,下界和切割的有效性。最后,通过一系列人工实例和实际算例对所提出的方法和算法进行了测试,验证了其实用性和获得高质量解的能力。
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引用次数: 0
To park or to share your autonomous vehicle? 停车还是共享你的自动驾驶汽车?
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-09 DOI: 10.1016/j.trb.2025.103305
Zhuoye Zhang , Fangni Zhang , Wei Liu
With the ability to drive autonomously during trips and park themselves, autonomous vehicles (AVs) are anticipated to revolutionize future mobility. How AVs interact with people and transform travel behavior patterns (mobility paradigm shift) is expected to be a “game changer”. This paper investigates an innovative future mobility paradigm where private-AV owners can share their vehicles on a mobility service platform when not in use. We develop tractable models to characterize the travel, parking, and vehicle-sharing choices of AV users, optimize operation strategies of the mobility service platform considering AV sharing, and evaluate their system-wide impacts. In particular, given the operation strategies of the mobility service platform, we formulate the system equilibrium that includes the AV owners’ choice equilibrium and the mobility service market equilibrium. We consider two different business formats for platform operator (namely reselling and commissioning) and three types of AV owners (risk-neutral, risk-averse or risk-seeking). Subject to the system equilibrium, we examine the pricing and fleet sizing strategies of the platform to achieve either profit-maximization or social welfare-maximization. Our analysis explores the impacts of introducing the AV sharing scheme on AV owners, mobility service operator and users, and social welfare. It shows that introducing the AV sharing scheme has the potential to create a win-win-win outcome for AV owners, mobility service operator, and users, with an overall improvement in social welfare. Moreover, both a social welfare-maximizing operator and a profit-maximizing operator may achieve a win-win-win outcome under certain conditions. With risk-averse AV owners, the reselling format proves to be superior to the commissioning format; with risk-seeking AV owners, the commissioning format will outperform the reselling format; while with risk-neutral AV owners, both formats can yield identical platform profit and social welfare. Numerical examples are presented to illustrate the analytical results and provide a deeper understanding of the potential implications of AV sharing.
由于能够在旅途中自动驾驶和自动停车,自动驾驶汽车(AVs)有望彻底改变未来的出行方式。自动驾驶汽车如何与人互动并改变出行行为模式(移动模式转变)有望成为“游戏规则改变者”。本文研究了一种创新的未来移动模式,即私人自动驾驶汽车车主可以在不使用时在移动服务平台上共享他们的车辆。我们开发了可操作的模型来描述自动驾驶汽车用户的出行、停车和车辆共享选择,优化考虑自动驾驶汽车共享的出行服务平台的运营策略,并评估其对系统的影响。特别是考虑到出行服务平台的运营策略,我们构建了包含自动驾驶汽车车主选择均衡和出行服务市场均衡的系统均衡。我们考虑了平台运营商的两种不同业务模式(即转售和调试)和三种类型的AV所有者(风险中性、风险厌恶或风险寻求)。在系统均衡的前提下,我们研究了平台的定价和车队规模策略,以实现利润最大化或社会福利最大化。我们的分析探讨了引入自动驾驶汽车共享计划对自动驾驶汽车车主、移动服务运营商和用户以及社会福利的影响。研究显示,引入自动驾驶汽车共享计划,可为自动驾驶汽车车主、移动服务营运商和使用者创造三赢的结果,并整体改善社会福利。而且,在一定条件下,社会福利最大化的经营者和利润最大化的经营者都可能实现三赢。对于风险厌恶的AV所有者,转售格式被证明优于委托格式;对于喜欢冒险的影音车主,委托模式的表现将优于转售模式;而对于风险中性的自动驾驶车主,两种模式都可以产生相同的平台利润和社会福利。文中给出了数值例子来说明分析结果,并对AV共享的潜在影响提供了更深入的理解。
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引用次数: 0
Integrated flexible transport service for passenger and freight under stochastic demand and service time 随机需求和服务时间下的客货综合灵活运输服务
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-09 DOI: 10.1016/j.trb.2025.103313
Enoch Lee , Manzi Li , Lubing Li , Hong K. Lo
The growth of e-commerce has increased the pressure on urban freight systems, exacerbating traffic congestion and environmental costs. Conversely, public transport often has underutilized capacity, which presents an opportunity for freight transport. Building on this potential, we propose an integrated flexible transport system that serves both passenger and freight. We develop a two-stage stochastic optimization model that accounts for uncertainties in demand location, servie time, and volume for the integrated system. The flexible bus routes are strategically planned in the first stage, and actual passenger and freight orders are assigned to each bus in the second stage. To solve the problem, a reliability-based decomposition method is proposed to optimize reliability measures, determine the optimal flexible transport route, and minimize costs. Numerical studies show that integrating freight and passenger operations reduces costs by 12 %, while accounting for stochasticity reduces costs by 11.8 % compared to deterministic models. A case study in Manhattan validates the model's scalability and effectiveness in large-scale, real-world setting.
电子商务的发展增加了城市货运系统的压力,加剧了交通拥堵和环境成本。相反,公共交通的运力往往没有得到充分利用,这就为货运提供了机会。在这一潜力的基础上,我们提出了一个同时服务客运和货运的综合灵活运输系统。我们开发了一个两阶段随机优化模型,该模型考虑了集成系统在需求位置、服务时间和容量方面的不确定性。第一阶段对灵活的公交路线进行战略规划,第二阶段对每辆公交分配实际的客货订单。针对这一问题,提出了一种基于可靠性的分解方法,优化可靠性措施,确定最优的柔性运输路线,使成本最小化。数值研究表明,与确定性模型相比,综合货运和客运运营的成本降低了12% %,而考虑随机性的成本降低了11.8% %。曼哈顿的一个案例研究验证了该模型在大规模现实环境中的可扩展性和有效性。
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引用次数: 0
Comparison of compact formulations for the electric vehicle routing problem 电动汽车路径问题紧凑公式的比较
IF 6.3 1区 工程技术 Q1 ECONOMICS Pub Date : 2025-09-09 DOI: 10.1016/j.trb.2025.103314
Zhiguo Wu , Hande Yaman
The electric vehicle routing problem is an extension of the capacitated vehicle routing problem, where en-route recharging needs to be addressed due to the limited driving range of electric vehicles. In this study, we compare four compact formulations that differ in the way they model the battery consumption. The first two formulations use Miller–Tucker–Zemlin’s approach, while the last two use single-commodity flows for this purpose. Within each approach, the two formulations have distinct ways of dealing with the fact that recharging stations may be visited more than once. In particular, two formulations make use of arcs that correspond to two-leg paths with a recharging station in the middle, whereas the other two formulations use copies of recharging stations, as suggested in the literature. We compare the linear programming bounds of these four formulations as well as the existing formulations from a theoretical point of view. Then, we analyze the performance of the new and existing formulations using six sets of benchmark instances. The computational results show that our formulations tighten the linear programming bounds and require less computation time to prove optimality.
电动汽车路径问题是有容车辆路径问题的延伸,由于电动汽车行驶里程有限,需要解决途中充电问题。在这项研究中,我们比较了四种紧凑的配方,不同的方式,他们模拟电池消耗。前两个公式使用米勒-塔克-泽姆林的方法,而最后两个公式使用单一商品流来实现这一目的。在每一种方法中,这两种方案都有不同的方法来处理充电站可能被访问不止一次的事实。特别地,两种配方使用了两条腿路径对应的弧线,中间有一个充电站,而其他两种配方使用了充电站的副本,如文献中所建议的。我们从理论上比较了这四种表述的线性规划界以及现有表述的线性规划界。然后,我们使用六组基准实例分析了新公式和现有公式的性能。计算结果表明,我们的公式收紧了线性规划边界,证明最优性所需的计算时间较少。
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引用次数: 0
期刊
Transportation Research Part B-Methodological
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