論文速遞 | Transportation Science 5-6月文章精選

來源：市場資訊

（來源：運籌OR帷幄）

推文作者：劉一達

編者按

在本文章中，我們對頂刊《Transportation Science》于2026年5-6月份在線發布的文章中進行了梳理（共9篇），并總結其基本信息，旨在幫助讀者快速洞察行業最新動態。近兩月TS發文聚焦智慧物流、平臺經濟、城市客運管理與交通大模型應用，研究冷鏈與準時制供應鏈路徑優化、外賣中轉與眾包配送機制、應急物資網絡規劃、通勤瓶頸動態演化等前沿問題。方法涵蓋Benders分解等精確優化算法、組合拍賣機制、分層強化學習與畫像嵌入學習等先進技術。

● 題目：An Exact Algorithm for the Vehicle Routing Problem with Time Windows and Perishable Products

考慮帶時間窗與易腐貨物的車輛路徑問題精確算法

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0262

● 作者：Selin Hülagü , Claudio Ciancio, Said Dabia , Wout Dullaert

● 發布時間：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.

在配送過程中，保持溫控易腐貨物的質量至關重要。諸多因素都會影響配送期間的產品質量和制冷能耗，其中包括送貨卡車內部溫度、路徑時長、停靠次數以及車輛載重。然而，現有關于易腐貨物路徑規劃的文獻往往僅考慮了這些因素中的有限一部分，且多數求解方法依賴于啟發式算法或商業求解器。

本研究針對考慮時間窗與質量約束的車輛路徑問題進行了建模。其目標是確定一組車輛路徑，在滿足客戶質量標準和時間窗的前提下，使行駛成本與制冷能耗成本之和最小。為了刻畫運輸過程中的產品質量衰減，我們提出了一個綜合考量溫度、路徑時長、?？看螖岛蛙囕v載重影響的函數，從而擴展了文獻中現有的質量衰減模型。為了求解該問題，我們開發了一個定制的精確求解框架，并通過引入若干專用特性來高效處理質量衰減與能耗成本函數。數值算例實驗表明，所提算法能夠有效求解規模達100個客戶的算例。此外，我們重新審視了溫控路徑規劃中的權衡關系，深入探討了質量衰減和溫度相關系數對路徑決策及成本的影響，并提供了實用的見解。

● 題目：Optimal Assignment of Shipments to Milk Runs for Just-in-Time Part Supply Under Uncertain Due Dates

交貨期不確定下準時制零部件供應的循環取貨貨物最優指派研究

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0189

● 作者：Julian Baals , Simon Emde , Ola Jabali

● 發布時間：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.

本研究關注一家為實施準時制生產的原始設備制造商組織入廠物流的物流服務商。該物流服務商定期執行循環取貨，即按照固定路線訪問部分供應商，以收集發往原始設備制造商的貨物。盡管循環取貨路線和大體的時間表早已提前確定，但貨物在制造商處的精確交貨期只有在生產序列最終敲定后才能獲知。在日常運營中，執行給定的循環取貨方案，從而從供應商處提取貨物并送達制造商，在理想情況下應完全實現準時制。然而，制造商裝配線上的生產序列在執行當天經常發生變化，這改變了貨物的交貨期，因此在將貨物指派給循環取貨車次時，有必要預先考慮潛在的干擾。

我們構建了一個兩階段隨機規劃模型：第一階段將貨物分配給特定的循環取貨車次；第二階段在生產序列的變化明朗后，調整到達時間并在必要時對貨物進行加急配送。該指派方案會根據每批貨物在制造商處不確定的交貨期產生提前或滯后成本，而加急配送則會產生固定成本。除了建立擴展形式的混合整數線性規劃模型外，我們還開發了一種基于整數L形法的求解程序，并通過引入源自部分Benders分解和子問題松弛的有效不等式與割平面來增強其性能。在基于現實測試數據的算例研究中，我們證明了所提L形法能夠將70個算例中的62個求解至最優。從管理視角來看，我們表明加急配送是緩解生產序列不確定性的有效途徑，重疊的循環取貨路線亦是如此——后者雖然在實際中尚未得到廣泛應用，但相對容易實施。

● 題目：Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability

考慮參數異質性的出發時間選擇：均衡與不穩定性

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0109

● 作者：Hillel Bar-Gera , Stephen Boyles, Liron Ravner

● 發布時間：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.

維克里經典的單瓶頸出發時間選擇均衡模型在許多合理的逐日學習動力學下都會表現出不穩定性。然而，這種不穩定性在現實中并未被觀察到，那么這一現實與理論的差異究竟是源于逐日動力學本身，還是源于基礎模型的某個簡化假設？

本文探討了基礎模型的一種變體，該變體引入了計劃延誤參數的連續分布，直觀上我們預期它會具備更優的穩定性特征。為了確保模型的可解性，我們假設了提前參數與滯后參數之間存在單調關系。我們首先驗證了該模型均衡解的存在性與唯一性。隨后，我們研究了一類廣泛的、滿足局部壓力和序保持條件的逐日動力學。我們的核心貢獻在于通過嚴謹的數學證明闡明了一個出人意料的結論：在此情境下，所有這類逐日動力學實際上都是不穩定的。

● 題目：Short-Term Rolling Stock Scheduling and Platform Assignment: A Branch-and-Check Method

短期車底運用計劃與站臺指派的協同調整：一種分支檢查法

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0291

● 作者：Lin Yang , Yuan Gao , Valentina Cacchiani , Suxiu Xu , Huiling Fu

● 發布時間：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.

鐵路客運需求受重大活動、節假日以及旅客個人出行行為的影響而頻繁波動，難以提前數月進行精準預測。面向市場的鐵路運輸計劃通常會根據短期預測的客運需求，采取取消或增開列車車次的策略。這導致需要以天為單位，對車底運用計劃（RSS）和列車站臺指派方案（TPP）進行動態調整。車底運用計劃確定了動車組（TUs）的運行表，即每組動車組將要執行的車次序列以及必須接受的檢修任務。站臺指派方案則確定了站臺對動車組的分配：當同一組動車組連續執行兩個車次時，必須為其指派一個站臺以完成車次銜接。

由于需求波動，需要調整車底運用計劃以執行一組與原計劃不同的車次，這就要求重新構建動車組的車次序列并重新安排其檢修計劃；同時，還必須修改站臺指派方案，以確保執行新車次序列的動車組能獲得可行的站臺指派。為了協助鐵路部門做出優化決策，本研究通過提出一個整數線性規劃模型和一種精確分解算法，對車底運用計劃與站臺指派方案的協同調整進行了研究。該協同模型由兩部分組成：(i) 考慮檢修約束的車底運用調度，以及 (ii) 站臺指派。其目標是最小化運營成本以及與原計劃的偏離度。該分解算法采用一種分支檢查（B&C）法，其中檢修約束和站臺指派通過動態割平面生成技術進行處理，并融入了針對特定問題的加速技術以縮減搜索空間和計算時間。

所提分支檢查法在中國高速鐵路系統的真實算例上進行了測試，涉及多達981個車次，結果表明在1小時的計算時間內即可獲得最優解。結果表明，即使在中等規模的算例中，分支檢查法的性能也明顯優于利用通用求解器直接求解協同模型。此外，與先調整車底運用計劃、再計算新站臺指派方案的不同序貫方法進行對比，進一步凸顯了協同調整框架的優勢。

● 題目：Enhancing Online Food Delivery with Transfer Points: A Data-Driven Decompose-Then-Optimize Approach

基于中轉點優化的在線外賣配送：一種數據驅動的先分解后優化方法

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0147

● 作者：Xinyuan Zhang , Qi Luo , Xinwu Qian

● 發布時間：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.

在線外賣配送平臺可以通過在中間中轉點整合具有相似起點、終點和時間窗的訂單來提升運營效率。本研究探討了考慮中轉的在線外賣配送問題，并評估了基于中轉的路徑規劃與騎手分配對提升配送績效的作用。我們提出了一個新型的數據驅動“先分解后優化”框架，該框架能夠有效抑制因中轉和同步決策導致的路徑空間指數級增長，從而支持近實時決策。

該分解策略將第一階段的涉中轉路徑規劃與指派子問題，同第二階段易于求解的廣義線性指派問題相結合。我們開發了一個定制的分層強化學習模型來學習該策略，并針對性地解決了分層強化學習以及涉中轉外賣配送問題固有的學習瓶頸。數值實驗表明，相比于目前最先進的啟發式算法和不考慮中轉的基線方案，該模型分別使系統凈收益提升了13.3%和26.9%。我們進一步分析了中轉訂單的運營特征，以及騎手異質性對系統性能的影響。將該模型應用于美團的真實數據中，結果表明，相比于優化后的傳統無中轉運營，系統營收提升了16.1%，同時所需的騎手規模縮減了11.48%。綜上所述，該框架通過引入中轉機制和提高騎手利用率提供了一種實時求解方案，為構建更具可持續性與擴展性的外賣配送系統提供了有力支撐。

● 題目：Auction Mechanism Design for Order Allocation and Payment in a Crowdshipping System

眾包配送系統中訂單分配與支付的拍賣機制設計

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0089

● 作者：Qingyang Li , Fangni Zhang

● 發布時間：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.

眾包配送已成為一種新型的服務模式，它通過招募社會出行大眾在日常行程中順路遞送包裹，從而有效利用了交通系統中的富余運力。為了激勵異質性出行者參與眾包承運，本研究針對一個集成了眾包配送與專職配送服務的眾包物流系統，提出了有效的拍賣機制。在該系統中，中介平臺向客戶收取服務費，并向潛在的眾包承運人征集報價。根據拍賣結果，平臺要么向中標者分配訂單并支付報酬，要么將訂單外包給專職配送服務。

我們設計了一種單邊密封價格組合拍賣機制，用以分配訂單并確定眾包承運人的報酬。該拍賣程序允許承運人針對與其原始出行路線相契合的訂單組合提交互斥報價。我們應用 VCG 機制來實現分配效率和抗策略性。為了提升大規模求解能力，我們還設計了一種將貪心分配與次優定價策略相結合的近似機制。該貪心機制提供了系統總成本的上界，并滿足事后遺憾有界的近似抗策略性。只有當眾包承運人對某些訂單組合進行虛高報價時，才會產生正的事后遺憾，且其大小以該承運人在不真實報價下所分配組合的真實成本節約量為上界。在相同的溫和條件下，兩種機制均能保證平臺利潤非負。

分析表明，平臺可以通過限制每位眾包承運人的最大報價數以及每個組合中的最大訂單數，來有效調節兩種拍賣機制的性能。為了更有效地削減成本，建議平臺在訂單數量顯著超過眾包承運人數量時舉行拍賣。本文開發的兩種拍賣機制還可以應用于更一般的情境，即供應商對物品組合提交報價，且每件物品都存在一個固定價格的備用選項。

● 題目：Time-Phased Relief Supply Network Planning for Foreseen Disasters

可預見災害下分階段救援物資供應網絡規劃

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0217

● 作者：Vala Rahmati , Halit üster

● 發布時間：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.

本研究探討了針對颶風和洪水等可預見災害的應急準備工作。以具有成本效益的方式及時供應救援物資，開展合理的準備與規劃，是決定災后恢復速度以及能否最大程度減輕受災群眾痛苦的關鍵因素。在假設大量避難所位置進行局部聚合的前提下，我們旨在確定救援物資分銷中心的位置，并規劃從有容量限制的分銷中心到各避難所的物資運輸路徑，依托底層的分階段網絡來實現具有成本效益的及時配送。

在滿足避難所最壞情況需求的假設下，我們提出了一個混合整數優化模型來解決該問題。為了求解該模型，我們開發了一種基于Benders分解的高效算法。該算法通過主問題解的修正以及引入多種代理約束等增強技術，有效解決了獲取最優性割平面的挑戰。我們在廣泛的隨機生成測試數據集上測試了這些增強技術的性能，以找出最有效的方法。最后，我們將該模型和求解算法應用于德克薩斯州南部的實際案例研究中，相關數據由地理信息系統進行集成和管理。我們借此檢驗了各種輸入參數對救援網絡設計和戰術運營的影響，并對模型進行了進一步的驗證與確認。

● 題目：Aligning LLM with Humans for Travel Choices: A Persona-Based Embedding Learning Approach

大語言模型與人類出行選擇的對齊：一種基于畫像的嵌入學習方法

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0330

● 作者：Tianming Liu , Manzi Li , Yafeng Yin

● 發布時間：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.

大語言模型通過作為人類代理，在推動出行需求建模方面展現出巨大的潛力，但它們與人類出行者之間的行為不一致仍然是一個關鍵障礙。此外，當現有的對齊方法應用于出行選擇中常見的稀疏數據集時，往往顯得不切實際或效率低下，從而限制了這些強大新工具的應用。

我們提出了一個全新的框架，用于實現大語言模型與出行選擇行為的對齊。該方法首先從實證數據中推斷出一組出行者畫像，然后估計一個畫像載荷函數，該函數利用學到的嵌入表征，根據個體的社會人口統計特征為其選擇合適的畫像。通過在Swissmetro交通方式選擇數據集上的驗證，我們的方法在預測宏觀和個體選擇結果方面，均顯著優于已有的基準模型。本研究為基于大語言模型的穩健出行行為模擬提供了一條更具適應性、可解釋性且資源高效的途徑，為未來將大語言模型融入交通建模實踐奠定了基礎。

● 題目：The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms

無向團隊定向弧路由問題：模型、有效不等式與精確算法

● 原文鏈接：https://doi.org/10.1287/trsc.2025.0155

● 作者：Wenjin Yan , Elena Fernández , Ivana Ljubi?

● 發布時間：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.

我們引入了無向團隊定向弧路由問題的一個新變體，該變體集成了三個關鍵特征：必經邊、有容量限制的車輛以及多種服務。這些特征在現有文獻中均被單獨探討過，但尚未被同時納入考量。在該問題中，需求分布在給定無向圖的某些邊上，服務這些有需求的邊會產生利潤?？尚新窂奖仨殢慕o定的車廠出發并返回該車廠，且每條路徑的最大行駛時間受到限制，每輛車服務的需求總量也受到容量限制。該問題旨在尋找一組最多包含固定數量路徑的方案，在確保所有必經邊均得到服務的同時實現總利潤最大化。

我們利用該問題的最優性條件，提出了一個基于二元變量的新型統一無向數學模型。隨后，我們基于該模型引入了基于邏輯的 Benders 分解方法，實現了問題的新型重構，并闡明了如何對基于邏輯的 Benders 割平面進行增強。至關重要的是，無論上述特征如何組合啟用，Benders 子問題的結構均保持不變，這突顯了該方法出色的模塊化與靈活性。此外，我們設計了幾類新型有效不等式，其中部分不等式是基于沖突圖推導而來的。

我們進行了廣泛的數值算例測試，以檢驗所提模型和有效不等式在不同設定下的性能表現。我們還進一步分析了一個現實世界算例的解結構，以闡明不同特征在實際應用中的具體影響。研究結果強調了基于邏輯的 Benders 分解和沖突圖在求解該問題中的核心作用。據我們所知，這也是上述方法首次被應用于弧路由問題領域。此外，這些技術也有望為更廣泛的弧路由問題提供更先進的求解思路。

「運籌OR帷幄」原創的《魯棒優化入門》電子書正在GitHub更新中，歡迎復制鏈接閱讀

https://github.com/Operations-Research-Science/Ebook-An_introduction_to_robust_optimization