来源：市场资讯
（来源：运筹OR帷幄）
推文作者：刘一达
编者按
在本文章中，我们对顶刊《Transportation Science》于2026年5-6月份在线发布的文章中进行了梳理（共9篇），并总结其基本信息，旨在帮助读者快速洞察行业最新动态。近两月TS发文聚焦智慧物流、平台经济、城市客运管理与交通大模型应用，研究冷链与准时制供应链路径优化、外卖中转与众包配送机制、应急物资网络规划、通勤瓶颈动态演化等前沿问题。方法涵盖Benders分解等精确优化算法、组合拍卖机制、分层强化学习与画像嵌入学习等先进技术。
● 题目：An Exact Algorithm for the Vehicle Routing Problem with Time Windows and Perishable Products
考虑带时间窗与易腐货物的车辆路径问题精确算法
● 原文链接：https://doi.org/10.1287/trsc.2025.0262
● 作者：Selin Hülagü , Claudio Ciancio, Said Dabia , Wout Dullaert
● 发布时间：2026-5-4
● 摘要：
Maintaining the quality of temperature-controlled perishable products during distribution is essential. Several factors affect product quality and the energy cost of refrigeration during distribution, including the temperature inside delivery trucks, route duration, number of stops, and vehicle load. The existing literature on routing for perishable products considers only a limited set of these factors, and most solution methods rely on heuristics or commercial solvers. This research formulates a vehicle routing problem with time windows and quality considerations. The objective is to determine a set of vehicle routes that minimize both travel costs and refrigeration energy costs while satisfying customer quality criteria and time windows. To capture product quality decay during transportation, we propose a function that accounts for the effect of temperature, route duration, number of stops, and vehicle load, thereby extending existing quality decay models in the literature. To solve the problem, we developed a tailored exact framework with several specialized features to efficiently manage quality decay and energy cost functions. Computational experiments demonstrate that the proposed algorithm is capable of solving instances with up to 100 customers. In addition, we revisit the trade-offs in temperature-controlled routing and provide useful insights into the impact of quality decay and temperature-related coefficients on routing decisions and costs.
在配送过程中，保持温控易腐货物的质量至关重要。诸多因素都会影响配送期间的产品质量和制冷能耗，其中包括送货卡车内部温度、路径时长、停靠次数以及车辆载重。然而，现有关于易腐货物路径规划的文献往往仅考虑了这些因素中的有限一部分，且多数求解方法依赖于启发式算法或商业求解器。
本研究针对考虑时间窗与质量约束的车辆路径问题进行了建模。其目标是确定一组车辆路径，在满足客户质量标准和时间窗的前提下，使行驶成本与制冷能耗成本之和最小。为了刻画运输过程中的产品质量衰减，我们提出了一个综合考量温度、路径时长、停靠次数和车辆载重影响的函数，从而扩展了文献中现有的质量衰减模型。为了求解该问题，我们开发了一个定制的精确求解框架，并通过引入若干专用特性来高效处理质量衰减与能耗成本函数。数值算例实验表明，所提算法能够有效求解规模达100个客户的算例。此外，我们重新审视了温控路径规划中的权衡关系，深入探讨了质量衰减和温度相关系数对路径决策及成本的影响，并提供了实用的见解。
● 题目：Optimal Assignment of Shipments to Milk Runs for Just-in-Time Part Supply Under Uncertain Due Dates
交货期不确定下准时制零部件供应的循环取货货物最优指派研究
● 原文链接：https://doi.org/10.1287/trsc.2025.0189
● 作者：Julian Baals , Simon Emde , Ola Jabali
● 发布时间：2026-5-22
● 摘要：
We focus on a logistics service provider (LSP) that organizes the inbound logistics for an original equipment manufacturer (OEM) using just-in-time production. The LSP conducts periodic milk runs, that is, tours visiting a subset of suppliers on a fixed route to collect shipments bound for the OEM. Although the milk-run routes and rough schedules are fixed well in advance, the exact shipment due dates at the OEM become known only once the production sequence has been finalized. During daily operation, the given milk runs are executed such that shipments are picked up from the suppliers and delivered to the OEM ideally exactly just in time. However, the production sequence on the assembly lines at the OEM often changes on the day of execution, which alters shipment due dates at the OEM and makes it necessary to anticipate potential disturbances when assigning shipments to milk runs. We formulate a two-stage stochastic program, where, in the first stage, shipments are assigned to specific milk runs and, in the second stage, when alterations to the production sequence are revealed, arrival times are adjusted and shipments are express delivered if necessary. The assignment induces earliness–tardiness costs depending on the uncertain due date of each shipment at the OEM, and express deliveries induce fixed costs. Besides an extensive-form mixed-integer linear program, we develop a solution procedure based on the integer L-shaped method, enriched with valid inequalities and cuts derived from partial Benders decomposition and a subproblem relaxation. In a computational study on realistic test data, we show that the proposed L-shaped method solves 62 out of 70 instances to optimality. From a managerial perspective, we show that express deliveries are an effective way of mitigating uncertainty in the production sequence, as are overlapping milk-run routes, which are not yet widely used in practice but are relatively easy to implement.
本研究关注一家为实施准时制生产的原始设备制造商组织入厂物流的物流服务商。该物流服务商定期执行循环取货，即按照固定路线访问部分供应商，以收集发往原始设备制造商的货物。尽管循环取货路线和大体的时间表早已提前确定，但货物在制造商处的精确交货期只有在生产序列最终敲定后才能获知。在日常运营中，执行给定的循环取货方案，从而从供应商处提取货物并送达制造商，在理想情况下应完全实现准时制。然而，制造商装配线上的生产序列在执行当天经常发生变化，这改变了货物的交货期，因此在将货物指派给循环取货车次时，有必要预先考虑潜在的干扰。
我们构建了一个两阶段随机规划模型：第一阶段将货物分配给特定的循环取货车次；第二阶段在生产序列的变化明朗后，调整到达时间并在必要时对货物进行加急配送。该指派方案会根据每批货物在制造商处不确定的交货期产生提前或滞后成本，而加急配送则会产生固定成本。除了建立扩展形式的混合整数线性规划模型外，我们还开发了一种基于整数L形法的求解程序，并通过引入源自部分Benders分解和子问题松弛的有效不等式与割平面来增强其性能。在基于现实测试数据的算例研究中，我们证明了所提L形法能够将70个算例中的62个求解至最优。从管理视角来看，我们表明加急配送是缓解生产序列不确定性的有效途径，重叠的循环取货路线亦是如此——后者虽然在实际中尚未得到广泛应用，但相对容易实施。
● 题目：Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability
考虑参数异质性的出发时间选择：均衡与不稳定性
● 原文链接：https://doi.org/10.1287/trsc.2025.0109
● 作者：Hillel Bar-Gera , Stephen Boyles, Liron Ravner
● 发布时间：2026-5-27
● 摘要：
Vickrey’s classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality, so does this difference stem from the day-to-day dynamics or from one of the simplifying assumptions of the basic model? This paper explores a variant of the basic model with a continuous distribution of schedule delay parameters, which we intuitively expect to have more favorable stability properties. To attain tractability, we assume a monotonic relationship between earliness and lateness parameters. We first verify the existence and uniqueness of the equilibrium solution for this model. We then study a broad class of day-to-day dynamics satisfying local pressure and order preservation conditions. Our main contribution is a formal proof that, surprisingly, all such day-to-day dynamics in this context are unstable.
维克里经典的单瓶颈出发时间选择均衡模型在许多合理的逐日学习动力学下都会表现出不稳定性。然而，这种不稳定性在现实中并未被观察到，那么这一现实与理论的差异究竟是源于逐日动力学本身，还是源于基础模型的某个简化假设？
本文探讨了基础模型的一种变体，该变体引入了计划延误参数的连续分布，直观上我们预期它会具备更优的稳定性特征。为了确保模型的可解性，我们假设了提前参数与滞后参数之间存在单调关系。我们首先验证了该模型均衡解的存在性与唯一性。随后，我们研究了一类广泛的、满足局部压力和序保持条件的逐日动力学。我们的核心贡献在于通过严谨的数学证明阐明了一个出人意料的结论：在此情境下，所有这类逐日动力学实际上都是不稳定的。
● 题目：Short-Term Rolling Stock Scheduling and Platform Assignment: A Branch-and-Check Method
短期车底运用计划与站台指派的协同调整：一种分支检查法
● 原文链接：https://doi.org/10.1287/trsc.2025.0291
● 作者：Lin Yang , Yuan Gao , Valentina Cacchiani , Suxiu Xu , Huiling Fu
● 发布时间：2026-6-4
● 摘要：
Railway passenger demand fluctuates because of events, holidays, and individual traveler activities, making it difficult to predict several months in advance. Market-oriented railway plans feature strategies for canceling or adding train trips according to short-term forecasted passenger demand. This results in dynamic adjustments of the rolling stock schedule (RSS) and the train platforming plan (TPP) on a daily basis. The RSS defines the schedule of the train units (TUs), that is, the sequence of trips that each TU will execute and the maintenance appointments it has to undergo. The TPP defines the assignment of platforms to TUs: when two trips are executed in sequence by the same TU, a platform has to be assigned to the TU for the trip connection. Because of demand fluctuation, the RSS has to be adjusted to perform a set of trips different from those in the original plan, requiring new trip sequences and rescheduled maintenance appointments for the TUs, whereas the TPP has to be modified to guarantee the feasible assignment of the platforms to the TUs performing the newly defined trip sequences. To assist railway departments in making optimized decisions, this work studies the integrated adjustment of the RSS and TPP by proposing an integer linear programming model and an exact decomposition algorithm. The integrated model consists of two parts: (i) rolling stock scheduling with maintenance constraints, and (ii) platform assignment. The goal is to minimize the operating costs and the deviations from the original plan. The decomposition algorithm consists of a branch-and-check (B&C) method in which maintenance constraints and platform assignment are handled by dynamic cut generation, and problem-specific acceleration techniques are incorporated to reduce the search space and the computation times. The proposed B&C method is tested on real-world instances from the Chinese high-speed railway system, involving up to 981 trips, showing that optimal solutions are obtained within one hour of computation time. It is shown that the B&C method clearly outperforms solving the integrated model by a general-purpose solver even on medium-size instances. Furthermore, comparisons with different sequential methods, which firstly adjust the RSS and then compute a new TPP, highlight the benefits of the integrated framework.
铁路客运需求受重大活动、节假日以及旅客个人出行行为的影响而频繁波动，难以提前数月进行精准预测。面向市场的铁路运输计划通常会根据短期预测的客运需求，采取取消或增开列车车次的策略。这导致需要以天为单位，对车底运用计划（RSS）和列车站台指派方案（TPP）进行动态调整。车底运用计划确定了动车组（TUs）的运行表，即每组动车组将要执行的车次序列以及必须接受的检修任务。站台指派方案则确定了站台对动车组的分配：当同一组动车组连续执行两个车次时，必须为其指派一个站台以完成车次衔接。
由于需求波动，需要调整车底运用计划以执行一组与原计划不同的车次，这就要求重新构建动车组的车次序列并重新安排其检修计划；同时，还必须修改站台指派方案，以确保执行新车次序列的动车组能获得可行的站台指派。为了协助铁路部门做出优化决策，本研究通过提出一个整数线性规划模型和一种精确分解算法，对车底运用计划与站台指派方案的协同调整进行了研究。该协同模型由两部分组成：(i) 考虑检修约束的车底运用调度，以及 (ii) 站台指派。其目标是最小化运营成本以及与原计划的偏离度。该分解算法采用一种分支检查（B&C）法，其中检修约束和站台指派通过动态割平面生成技术进行处理，并融入了针对特定问题的加速技术以缩减搜索空间和计算时间。
所提分支检查法在中国高速铁路系统的真实算例上进行了测试，涉及多达981个车次，结果表明在1小时的计算时间内即可获得最优解。结果表明，即使在中等规模的算例中，分支检查法的性能也明显优于利用通用求解器直接求解协同模型。此外，与先调整车底运用计划、再计算新站台指派方案的不同序贯方法进行对比，进一步凸显了协同调整框架的优势。
● 题目：Enhancing Online Food Delivery with Transfer Points: A Data-Driven Decompose-Then-Optimize Approach
基于中转点优化的在线外卖配送：一种数据驱动的先分解后优化方法
● 原文链接：https://doi.org/10.1287/trsc.2025.0147
● 作者：Xinyuan Zhang , Qi Luo , Xinwu Qian
● 发布时间：2026-6-4
● 摘要：
Online food delivery platforms can improve efficiency by consolidating orders with similar origins, destinations, and time windows at intermediate transfer locations. This research investigates the online food delivery problem with transfer (OFDP-T) and assesses how transfer-based routes and courier assignments enhance delivery performance. We propose a novel data-driven decompose-then-optimize framework that tames the exponential growth in route space from transfer and synchronization decisions and supports near-real-time decision making. The decomposition policy couples a first-step transfer-related routing and assignment subproblem with a tractable second-step generalized linear assignment problem. We develop a tailored hierarchical reinforcement learning (HRL) model to learn this policy and explicitly address learning barriers inherent to HRL and to the transfer-involved food delivery problem. Numerical experiments show that the model improves system net revenue by 13.3% over the best-known heuristics and by 26.9% over the nontransfer baseline. We further analyze the operational characteristics of transferred orders and the impact of courier heterogeneity on system performance. Applied to real-world Meituan data, the model yields a 16.1% increase in system revenue and an 11.48% reduction in the required courier fleet relative to optimized nontransfer operations. The framework thus provides a real-time solution by leveraging transfers and improving courier utilization, ultimately supporting a more sustainable and scalable food delivery system.
在线外卖配送平台可以通过在中间中转点整合具有相似起点、终点和时间窗的订单来提升运营效率。本研究探讨了考虑中转的在线外卖配送问题，并评估了基于中转的路径规划与骑手分配对提升配送绩效的作用。我们提出了一个新型的数据驱动“先分解后优化”框架，该框架能够有效抑制因中转和同步决策导致的路径空间指数级增长，从而支持近实时决策。
该分解策略将第一阶段的涉中转路径规划与指派子问题，同第二阶段易于求解的广义线性指派问题相结合。我们开发了一个定制的分层强化学习模型来学习该策略，并针对性地解决了分层强化学习以及涉中转外卖配送问题固有的学习瓶颈。数值实验表明，相比于目前最先进的启发式算法和不考虑中转的基线方案，该模型分别使系统净收益提升了13.3%和26.9%。我们进一步分析了中转订单的运营特征，以及骑手异质性对系统性能的影响。将该模型应用于美团的真实数据中，结果表明，相比于优化后的传统无中转运营，系统营收提升了16.1%，同时所需的骑手规模缩减了11.48%。综上所述，该框架通过引入中转机制和提高骑手利用率提供了一种实时求解方案，为构建更具可持续性与扩展性的外卖配送系统提供了有力支撑。
● 题目：Auction Mechanism Design for Order Allocation and Payment in a Crowdshipping System
众包配送系统中订单分配与支付的拍卖机制设计
● 原文链接：https://doi.org/10.1287/trsc.2025.0089
● 作者：Qingyang Li , Fangni Zhang
● 发布时间：2026-6-5
● 摘要：
Crowdshipping has emerged as a novel service paradigm that leverages excess capacity in the transportation system by enlisting the traveling public, namely the “crowd”, to deliver parcels during their daily trips. To incentivize heterogeneous travelers as crowd carriers, this study proposes effective auction mechanisms for a crowdshipping system that integrates both crowdshipping and dedicated delivery services. An intermediary platform charges a service fare from customers and solicits bids from potential crowd carriers. Based on the auction outcome, the platform either allocates orders and makes payments to the winning bidders or outsources the orders to dedicated delivery services. We develop a single-sided sealed-bid combinatorial auction to allocate orders and determine compensation for crowd carriers. This auction procedure allows carriers to submit mutually exclusive bids for order bundles that align with their original travel routes. We apply the Vickrey-Clarke-Groves mechanism to achieve allocative efficiency and strategy-proofness. To enhance scalability, we also devise an approximation mechanism that combines greedy allocation with a second-best pricing policy. The greedy mechanism provides an upper bound on total system cost and satisfies approximate strategy-proofness with bounded ex post regret. A positive ex post regret can only arise when a crowd carrier overbids on certain bundles, and its magnitude is bounded by the true cost savings of the assigned bundle under misreporting. Under the same mild conditions, both mechanisms yield nonnegative platform profit. Our analysis shows that the platform can effectively tune the performance of both auction mechanisms by regulating the maximum number of bids per crowd carrier and the maximum number of orders per bundle. To achieve more effective cost reduction, the platform is advised to conduct auctions when the number of orders substantially exceeds the number of crowd carriers. The two auction mechanisms developed in this paper can be applied to a more general setting where suppliers submit bids on bundles of items and there exists a fixed-price backup option for each item.
众包配送已成为一种新型的服务模式，它通过招募社会出行大众在日常行程中顺路递送包裹，从而有效利用了交通系统中的富余运力。为了激励异质性出行者参与众包承运，本研究针对一个集成了众包配送与专职配送服务的众包物流系统，提出了有效的拍卖机制。在该系统中，中介平台向客户收取服务费，并向潜在的众包承运人征集报价。根据拍卖结果，平台要么向中标者分配订单并支付报酬，要么将订单外包给专职配送服务。
我们设计了一种单边密封价格组合拍卖机制，用以分配订单并确定众包承运人的报酬。该拍卖程序允许承运人针对与其原始出行路线相契合的订单组合提交互斥报价。我们应用 VCG 机制来实现分配效率和抗策略性。为了提升大规模求解能力，我们还设计了一种将贪心分配与次优定价策略相结合的近似机制。该贪心机制提供了系统总成本的上界，并满足事后遗憾有界的近似抗策略性。只有当众包承运人对某些订单组合进行虚高报价时，才会产生正的事后遗憾，且其大小以该承运人在不真实报价下所分配组合的真实成本节约量为上界。在相同的温和条件下，两种机制均能保证平台利润非负。
分析表明，平台可以通过限制每位众包承运人的最大报价数以及每个组合中的最大订单数，来有效调节两种拍卖机制的性能。为了更有效地削减成本，建议平台在订单数量显著超过众包承运人数量时举行拍卖。本文开发的两种拍卖机制还可以应用于更一般的情境，即供应商对物品组合提交报价，且每件物品都存在一个固定价格的备用选项。
● 题目：Time-Phased Relief Supply Network Planning for Foreseen Disasters
可预见灾害下分阶段救援物资供应网络规划
● 原文链接：https://doi.org/10.1287/trsc.2025.0217
● 作者：Vala Rahmati , Halit Üster
● 发布时间：2026-6-10
● 摘要：
We consider emergency preparedness for foreseen disasters such as hurricanes and flooding. Proper preparation and planning for timely relief supply in a cost-effective manner can be crucial determinants of how quickly recoveries occur and with the least suffering of the affected populations. Assuming a host of shelter locations aggregated locally, we are interested in determining relief supply locations (distribution centers [DCs]) and routing of supply from the capacitated DCs to the shelters on an underlying time-phased network for cost-effective timely delivery. We present a mixed integer optimization model to address this problem under the assumption of covering the worst case demand at the shelters. To solve our model, we develop an efficient Benders decomposition–based algorithm that handles the challenges of obtaining optimality cuts via master problem solution modifications and various surrogate constraints among other enhancement techniques. We test the performance of the enhancement techniques on an extensive randomly generated test data set to identify the most effective approach. We finally use our model and the solution algorithm on an actual case study in southern Texas data incorporated and managed by a geographical information system to examine the impact of various input parameters on the design and tactical operation of the relief networks as well as for further model verification and validation.
本研究探讨了针对飓风和洪水等可预见灾害的应急准备工作。以具有成本效益的方式及时供应救援物资，开展合理的准备与规划，是决定灾后恢复速度以及能否最大程度减轻受灾群众痛苦的关键因素。在假设大量避难所位置进行局部聚合的前提下，我们旨在确定救援物资分销中心的位置，并规划从有容量限制的分销中心到各避难所的物资运输路径，依托底层的分阶段网络来实现具有成本效益的及时配送。
在满足避难所最坏情况需求的假设下，我们提出了一个混合整数优化模型来解决该问题。为了求解该模型，我们开发了一种基于Benders分解的高效算法。该算法通过主问题解的修正以及引入多种代理约束等增强技术，有效解决了获取最优性割平面的挑战。我们在广泛的随机生成测试数据集上测试了这些增强技术的性能，以找出最有效的方法。最后，我们将该模型和求解算法应用于德克萨斯州南部的实际案例研究中，相关数据由地理信息系统进行集成和管理。我们借此检验了各种输入参数对救援网络设计和战术运营的影响，并对模型进行了进一步的验证与确认。
● 题目：Aligning LLM with Humans for Travel Choices: A Persona-Based Embedding Learning Approach
大语言模型与人类出行选择的对齐：一种基于画像的嵌入学习方法
● 原文链接：https://doi.org/10.1287/trsc.2025.0330
● 作者：Tianming Liu , Manzi Li , Yafeng Yin
● 发布时间：2026-6-16
● 摘要：
Many business settings involve fluid teams, where team members come together to work on a project, after which the team is disbanded. It is well-known that coordination can be challenging and affect the performance outcomes of fluid teams. The literature has studied how several facets of experience can facilitate learning and improve outcomes for fluid teams. However, the role of experience with success and failure and its effect on improving outcomes for fluid teams has remained unexplored. In this study, we use data from the motion picture industry to examine how the experience with success and failure resident within key members of a movie production team affects profitability. Our analysis of the data for 2,091 movies released in the United States between 1999 and 2018 reveals that a movie’s profitability depends on the production team’s history with success and failure. Additionally, we find that teams with a history of success result in movies with higher profits, whereas teams with a history of failure result in movies with lower profits. We also find that increased relative dispersion in the team’s experience does not affect the movie’s profitability. Further analysis of the composition of movie teams indicates that financial performance can be significantly impacted when movie teams are predominantly composed of members with a history of success or failure. We contribute by illustrating a new measure of team experience relevant for fluid teams and by providing insights on how to compose teams based on members’ experience with success and failure.
大语言模型通过作为人类代理，在推动出行需求建模方面展现出巨大的潜力，但它们与人类出行者之间的行为不一致仍然是一个关键障碍。此外，当现有的对齐方法应用于出行选择中常见的稀疏数据集时，往往显得不切实际或效率低下，从而限制了这些强大新工具的应用。
我们提出了一个全新的框架，用于实现大语言模型与出行选择行为的对齐。该方法首先从实证数据中推断出一组出行者画像，然后估计一个画像载荷函数，该函数利用学到的嵌入表征，根据个体的社会人口统计特征为其选择合适的画像。通过在Swissmetro交通方式选择数据集上的验证，我们的方法在预测宏观和个体选择结果方面，均显著优于已有的基准模型。本研究为基于大语言模型的稳健出行行为模拟提供了一条更具适应性、可解释性且资源高效的途径，为未来将大语言模型融入交通建模实践奠定了基础。
● 题目：The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms
无向团队定向弧路由问题：模型、有效不等式与精确算法
● 原文链接：https://doi.org/10.1287/trsc.2025.0155
● 作者：Wenjin Yan , Elena Fernández , Ivana Ljubić
● 发布时间：2026-6-16
● 摘要：
We introduce a new variant of the Undirected Team Orienteering Arc Routing Problem (UTOARP) that incorporates three key features: required edges, capacitated vehicles, and multiple services. These features have been investigated individually in the literature but have not been considered simultaneously. In this problem, demand is placed at some edges of a given undirected graph, and served demand edges produce a profit. Feasible routes must start and end at a given depot, and there is a time limit on the maximum duration of each route and a capacity limit on the demand served by each vehicle. The problem asks for a set of up to |K| maximum profit routes while ensuring all required edges are served. We exploit optimality conditions for this problem and propose a new unified, undirected formulation with binary variables. We also introduce a logic-based Benders decomposition derived from this formulation, resulting in a new problem reformulation, and show how to strengthen the logic-based Benders cuts. Crucially, the structure of the Benders subproblems remains unchanged regardless of which of the above features are enabled, highlighting the modularity and flexibility of the approach. Furthermore, we design several new families of valid inequalities, where some of them are derived from conflict graphs. Extensive computational tests are conducted to examine the performance of the proposed formulations and valid inequalities under various settings. We further analyze the solution structure of a real-world instance to illustrate the practical impact of the different features. Our findings highlight the pivotal role of logic-based Benders decomposition and conflict graphs in solving the UTOARP, marking their first application in the context of arc routing problems to the best of our knowledge. Moreover, these techniques hold promise for advancing solution approaches in broader arc routing contexts.
我们引入了无向团队定向弧路由问题的一个新变体，该变体集成了三个关键特征：必经边、有容量限制的车辆以及多种服务。这些特征在现有文献中均被单独探讨过，但尚未被同时纳入考量。在该问题中，需求分布在给定无向图的某些边上，服务这些有需求的边会产生利润。可行路径必须从给定的车厂出发并返回该车厂，且每条路径的最大行驶时间受到限制，每辆车服务的需求总量也受到容量限制。该问题旨在寻找一组最多包含固定数量路径的方案，在确保所有必经边均得到服务的同时实现总利润最大化。
我们利用该问题的最优性条件，提出了一个基于二元变量的新型统一无向数学模型。随后，我们基于该模型引入了基于逻辑的 Benders 分解方法，实现了问题的新型重构，并阐明了如何对基于逻辑的 Benders 割平面进行增强。至关重要的是，无论上述特征如何组合启用，Benders 子问题的结构均保持不变，这突显了该方法出色的模块化与灵活性。此外，我们设计了几类新型有效不等式，其中部分不等式是基于冲突图推导而来的。
我们进行了广泛的数值算例测试，以检验所提模型和有效不等式在不同设定下的性能表现。我们还进一步分析了一个现实世界算例的解结构，以阐明不同特征在实际应用中的具体影响。研究结果强调了基于逻辑的 Benders 分解和冲突图在求解该问题中的核心作用。据我们所知，这也是上述方法首次被应用于弧路由问题领域。此外，这些技术也有望为更广泛的弧路由问题提供更先进的求解思路。
「运筹OR帷幄」原创的《鲁棒优化入门》电子书正在GitHub更新中，欢迎复制链接阅读
https://github.com/Operations-Research-Science/Ebook-An_introduction_to_robust_optimization
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