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    <title>Transport Research International Documentation (TRID)</title>
    <link>https://trid.trb.org/</link>
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
    <docs>http://blogs.law.harvard.edu/tech/rss</docs>
    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Transport Research International Documentation (TRID)</title>
      <url>https://trid.trb.org/Images/PageHeader-wTitle.jpg</url>
      <link>https://trid.trb.org/</link>
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    <item>
      <title>Multi-Modal Last-Mile Delivery Optimization With Smart Micro-Hubs: A Branch-and-Price Approach With Valid Inequalities</title>
      <link>https://trid.trb.org/View/2658732</link>
      <description><![CDATA[The rapid growth of e-commerce and urban logistics has intensified the challenges associated with last-mile delivery, necessitating the integration of autonomous delivery vehicles (ADVs), drones, and smart micro-hubs for cost-effective and sustainable operations. This study introduces a novel Multi-Depot Capacitated Vehicle Routing Problem with Time Windows and Multi-Modal Transportation (MD-CVRP-TW-MM), where deliveries are dynamically assigned to either ADVs or drones while optimizing hub locations and vehicle routing. The objective is to minimize total operational costs, including transportation, hub activation, and delivery mode selection, while ensuring service-level constraints such as time windows and capacity limits. To efficiently solve this complex combinatorial problem, we propose a mathematical formulation enhanced with valid inequalities for computational efficiency. Furthermore, a Branch-and-Price algorithm is developed, where column generation is employed to iteratively refine delivery routes while enforcing depot assignments and mode selection constraints. The solution approach integrates dual stabilization techniques and path-based heuristics to accelerate convergence. Experimental evaluations on benchmark datasets and real-world logistics scenarios demonstrate the effectiveness of the proposed method in reducing last-mile delivery costs, optimizing fleet utilization, and enhancing service reliability. The results highlight the significance of multi-modal last-mile delivery optimization in improving urban logistics and sustainability. This research contributes a new mathematical model, efficient optimization techniques, and practical insights for intelligent last-mile delivery planning in smart cities.]]></description>
      <pubDate>Thu, 19 Feb 2026 10:53:39 GMT</pubDate>
      <guid>https://trid.trb.org/View/2658732</guid>
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    <item>
      <title>Integrated Learning and Optimization for Joint Routing and Loading Decisions in Preowned Automobile Shipping</title>
      <link>https://trid.trb.org/View/2616181</link>
      <description><![CDATA[We study highway-based shipping of preowned automobiles by auto carriers, an important although overlooked problem in the automobile shipping literature. The special structure associated with auto carriers implies many different ways of loading a set of automobiles to an auto carrier with different loading costs. Thus, in addition to vehicle routing decisions, loading decisions are essential in automobile shipping optimization. The objective of our problem is to maximize the total revenue minus the total routing and loading cost subject to time windows and loading constraints among others. Most existing automobile shipping studies treat loading and routing separately; some studies partially address the loading aspect in routing optimization but only check the loading feasibility without evaluating the quality of loading decisions. We, thus, contribute to the literature by fully integrating loading decisions into routing decision making. An integrated machine learning (ML) and optimization approach is proposed to solve the problem. The overall approach follows a column generation–based solution framework, in which an insertion heuristic is proposed to find new routes based on existing routes, and ML is employed to predict the loading feasibility and estimate the minimum loading cost of a given route without solving the complex loading optimization problem. The integration of the ML approach and the insertion heuristic enables us to find high-quality new routes quickly in each column generation iteration. Two variants of this integrated approach are evaluated against a benchmark sequential approach in which routing and loading are tackled separately and another benchmark approach in which routing and loading are optimized jointly without using ML. Computational experiments demonstrate that the proposed integrated ML and optimization approach generates significantly better solutions than the sequential benchmark approach with only slightly more computation time and similar solutions to the joint optimization benchmark approach but with significantly less computation time. The proposed solution approach can be adopted by automobile shipping companies. It can also be adapted for other joint optimization problems, such as those in aircraft load planning.]]></description>
      <pubDate>Mon, 02 Feb 2026 09:33:48 GMT</pubDate>
      <guid>https://trid.trb.org/View/2616181</guid>
    </item>
    <item>
      <title>To ride or to fly: Optimal freight-on-transit operations using drones</title>
      <link>https://trid.trb.org/View/2567445</link>
      <description><![CDATA[With the rapid growth of e-commerce, urban areas are facing increasing congestion, particularly from last-mile deliveries. This challenge has prompted the exploration of innovative solutions. One such promising approach is freight-on-transit (FoT) operations, which utilize existing high-capacity urban transit networks to transport goods to designated transit stations, where more energy-efficient and flexible modes complete the last-mile delivery. This paper proposes a modeling framework for optimizing FoT operations using drones. The proposed mixed-integer linear program formulation accounts for fixed transit vehicle schedules, capacity constraints, and drone battery limitations. The problem is decomposed into a min-cost flow and drone vehicle routing problem with time windows, and a Lagrangian relaxation with a column generation algorithm is proposed as the solution method. Numerical experiments on hypothetical networks demonstrate the system’s effectiveness, highlighting the importance of buffer capacity in transit vehicles and extended drone battery life. A real-world case study in Chicago’s Metra system reveals significant cost savings and operational benefits compared to traditional truck-based or drone-only delivery methods.]]></description>
      <pubDate>Thu, 10 Jul 2025 16:39:44 GMT</pubDate>
      <guid>https://trid.trb.org/View/2567445</guid>
    </item>
    <item>
      <title>Learning-based column generation approach for the vehicle routing problem with release dates and incompatible loading constraints</title>
      <link>https://trid.trb.org/View/2562444</link>
      <description><![CDATA[This study introduces a variant of classical distribution problems, vehicle routing problems with release dates, and incompatible loading constraints (VRPR-ILC). The VRPR-ILC is derived from the practical application of a pharmaceutical distribution company based in China. It incorporates various real-world constraints, including release dates, product weights and volumes, incompatible loading, and time windows. The objective of the VRPR-ILC is to minimize the total travel distance. This variant can also find applications in diverse domains, such as e-commerce. Integrating the above constraints introduces the challenge of optimizing in both the temporal and spatial dimensions. To tackle this issue, the authors propose a learning-based column generation (LCG) approach. The LGG provides a new framework combining the deep learning (DL) technique with the column generation (CG) algorithm. By utilizing DL, the LCG effectively guides the CG in concentrating on the search space containing high-quality integer solutions. It helps to narrow the gap between linear and integer solutions and significantly enhances the convergence of the algorithm. Additionally, to address the challenges posed by the pricing problem of the VRPR-ILC, the authors develop the heuristic pricing, the dummy label dominance rule, and a lower bound evaluation strategy for labels. Computational results show that the LCG achieves competitive results compared with the GUROBI solver, the existing exact algorithm, and the heuristic algorithm. The results further indicate that utilizing the DL leads to improved solutions while reducing the time by 20%.]]></description>
      <pubDate>Tue, 08 Jul 2025 09:56:46 GMT</pubDate>
      <guid>https://trid.trb.org/View/2562444</guid>
    </item>
    <item>
      <title>Lookahead scenario relaxation for dynamic time window assignment in service routing</title>
      <link>https://trid.trb.org/View/2476373</link>
      <description><![CDATA[The authors consider a problem where customers dynamically request next-day home service, e.g., repair or installments. Unlike attended home delivery, customers cannot select a time window (TW), the service provider assigns a next-day TW to each new customer if the customer can feasibly be inserted in the service route of the next day without violating the TWs of the existing customers. Otherwise, customer service will be postponed to another day (which is outside the scope of this work). The provider aims to serve many customers the next day for fast service and efficient operations. Thus, TWs have to be assigned to keep the flexibility of the fleet for future requests. For such anticipatory assignments, the authors propose a stochastic lookahead method that samples a set of future request scenarios, solves the corresponding team-orienteering problems with TWs, and uses the solutions to evaluate current TW assignment decisions. For real-time solutions to the team orienteering problem, the authors propose to approximate its optimal solution value with an upper bound. The bound is obtained by solving the linear relaxation of a set packing reformulation via column generation. The authors test their algorithm on Iowa City data and compare it to several benchmark policies. The results show that our method significantly increases customer service, and the authors' relaxation is essential for effective decisions. The authors further show that their policy does not lead to observable discrimination against inconveniently located customers.]]></description>
      <pubDate>Mon, 27 Jan 2025 15:39:52 GMT</pubDate>
      <guid>https://trid.trb.org/View/2476373</guid>
    </item>
    <item>
      <title>A branch-and-price-and-cut algorithm for the home health care routing and scheduling problem with multiple prioritized time windows</title>
      <link>https://trid.trb.org/View/2414557</link>
      <description><![CDATA[This paper addresses a variant of home health care routing and scheduling problem with endogenous time window options for patients. The objective is to minimize the total operational cost while ensuring a specified level of service satisfaction regarding patients’ prioritized time windows. The authors formulate the problem as a set-covering model and propose a branch-and-price-and-cut (BPC) algorithm to tackle it. Specifically, the authors devise a column generation procedure to obtain the lower bounds in the branch-and-bound framework, in which they employ a labeling algorithm with a multiple time windows processing mechanism to deal with the pricing sub-problems. Additionally, the lower bound is strengthened by incorporating 2-path inequalities and subset-row inequalities. The effectiveness of the BPC algorithm is demonstrated through numerical experiments conducted on the modified Solomon benchmark instances. Furthermore, the authors analyze the problem and derive the following managerial insights: i) Incorporating the assignment decisions of time windows for patients into the problem can significantly reduce nurse costs and travel costs, even when accounting for patients’ preferences for time windows. ii) There is a negative correlation between cost savings and the overall satisfaction levels of patients’ preferred time windows, with marginal cost savings decreasing as the overall satisfaction level declines. iii) Besides the total satisfaction level, the operational cost is also influenced by factors such as the distribution of patient locations, the width of time windows, and the proportion of patients with multiple time windows.]]></description>
      <pubDate>Mon, 09 Sep 2024 09:56:01 GMT</pubDate>
      <guid>https://trid.trb.org/View/2414557</guid>
    </item>
    <item>
      <title>An exact algorithm for simultaneous pickup and delivery problem with split demand and time windows</title>
      <link>https://trid.trb.org/View/2404448</link>
      <description><![CDATA[This study introduces a new variant of the vehicle routing problem (VRP) called the simultaneous pickup and delivery problem with split demand and time windows (SPDP-SDTW). The motivation behind this study stems from real-life urban and rural delivery scenarios, encompassing features such as split demand, simultaneous pickup and delivery, many-to-many pickup and delivery, and time windows. The study thoroughly investigates the properties of the optimal solution for the SPDP-SDTW. Based on these properties, an arc flow model is developed for the SPDP-SDTW. Dantzig Wolfe (DW) decomposition techniques are employed to obtain the master problem and the pricing subproblem. In order to effectively address the SPDP-SDTW, an improved branch and price (I-BP) algorithm is proposed, incorporating a tailored column generation (CG) algorithm, branching strategies, and dual stabilization strategies. The proposed CG algorithm provides a framework that combines the improved adaptive degree heuristic (I-AGH) algorithm and the solver Gurobi. This integration substantially mitigates the computational burden involved in solving the subproblem. Extensive computational experiments conducted on datasets of varying sizes, including small, medium, and large instances, consistently demonstrate that the I-BP algorithm performs the best in both solution quality and computational efficiency when compared to existing exact and heuristic algorithms.]]></description>
      <pubDate>Wed, 14 Aug 2024 09:49:16 GMT</pubDate>
      <guid>https://trid.trb.org/View/2404448</guid>
    </item>
    <item>
      <title>Generalized Riskiness Index in Vehicle Routing under Uncertain Travel Times: Formulations, Properties, and Exact Solution Framework</title>
      <link>https://trid.trb.org/View/2413967</link>
      <description><![CDATA[The authors consider a vehicle routing problem with time windows under uncertain travel times where the goal is to determine routes for a fleet of homogeneous vehicles to arrive at the locations of customers within their stipulated time windows to the maximum extent while ensuring that the total travel cost does not exceed a prescribed budget. Specifically, a novel performance measure that accounts for the riskiness associated with late arrivals at the customers, called the generalized riskiness index (GRI), is optimized. The GRI covers several existing riskiness indices as special cases and generates new ones. The authors demonstrate its salient managerial and computational properties to motivate it better. The authors propose alternative set partitioning-based models of the problem. To obtain the optimal solution, the authors develop an exact solution framework combining route enumeration and branch-price-and-cut algorithms, in which the GRI is dealt with in route enumeration and column generation subproblems. The authors mainly reduce the solution space by exploiting the GRI and budget constraints’ properties without losing optimality. The proposed method is tested on a collection of instances derived from the literature. The results show that a new instance of the GRI outperforms several existing riskiness indices in mitigating lateness. The exact method can solve instances with up to 100 nodes to optimality. It can consistently solve instances involving up to 50 nodes, outperforming state-of-the-art methods by more than doubling the manageable instance size.]]></description>
      <pubDate>Wed, 07 Aug 2024 15:08:53 GMT</pubDate>
      <guid>https://trid.trb.org/View/2413967</guid>
    </item>
    <item>
      <title>A bidirectional branch-and-price algorithm with Pulse procedure for the Electric Vehicle Routing Problem with flexible deliveries</title>
      <link>https://trid.trb.org/View/2396007</link>
      <description><![CDATA[Delivery flexibility offers customers the convenience of receiving their orders at a location and time that best suits their schedule. Moreover, it enables delivery companies to better manage their operations and decrease costs. Nonetheless, this flexibility brings added complexities to route optimization. This study focuses on the Electric Vehicle Routing Problem with Flexible Deliveries, which becomes more challenging when the fleet comprises electric vehicles with limited autonomy. To solve this problem, the authors develop a novel column generation method embedded within a bidirectional branch-and-price algorithm enhanced with Pulse procedure. The authors adopt an enhanced bidirectional algorithm to solve the pricing subproblem to overcome common weaknesses of the classical labeling algorithms such as label storing. The BP is improved with state-of-the-art acceleration techniques including (i) a bidirectional search mechanism in which both forward and backward labels are created, (ii) a method to prevent solving the pricing sub-problem at each iteration, and (iii) an integer programming model that generates upper bounds. The authors present a new data set including instances with up to 120 customers and an extensive computational study evaluating the performance of the proposed BP algorithm. The authors' results show that the proposed algorithm can effectively solve instances with up to 60 customers, 237 delivery locations, and 13 recharging stations.]]></description>
      <pubDate>Tue, 23 Jul 2024 17:43:23 GMT</pubDate>
      <guid>https://trid.trb.org/View/2396007</guid>
    </item>
    <item>
      <title>An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station</title>
      <link>https://trid.trb.org/View/2379823</link>
      <description><![CDATA[This paper introduces a vehicle routing problem that simultaneously considers multiple trips, time windows, and a capacitated unloading station. This problem is a generalization of the multi-trip vehicle routing problem with time windows, which determines a set of least-cost vehicle routes to fulfill all customer demands while respecting the constraints of vehicle capacity and time windows. Due to restricted resources (e.g., equipment and labor force) at the depot, vehicles may need to wait in a queue for being unloaded when they arrive. This unloading capacity constraint significantly complicates the problem, as it causes a trip to involve three stages—traveling, waiting, and unloading. The authors formulate this problem as an arc flow model and a trip-based set partitioning model, where the latter is solved by a branch-price-and-cut (BPC) algorithm. To improve the computational aspect of the BPC framework, a two-phase column generation (CG) algorithm is designed. First, a bidirectional labeling algorithm is tailored to solve the pricing problem, where two accelerating strategies are employed to speed up the resolution process. Meanwhile, k-path inequalities and limited-memory subset row inequalities are utilized to tighten the linear relaxation of the master problem. Computational results based on the instances adapted from the well-known Solomon’s benchmark show that the developed BPC algorithm can solve most instances within 50 customers to optimality in a short time frame and some instances of 100 customers to optimality within a 3-hour time limit. Moreover, the authors' BPC algorithm performs better than exact algorithms in the literature for similar problem variants in both solution quality and computing time.]]></description>
      <pubDate>Thu, 13 Jun 2024 09:00:18 GMT</pubDate>
      <guid>https://trid.trb.org/View/2379823</guid>
    </item>
    <item>
      <title>Optimal autonomous truck platooning with detours, nonlinear costs, and a platoon size constraint</title>
      <link>https://trid.trb.org/View/2374264</link>
      <description><![CDATA[Autonomous trucks offer a promising avenue for enhancing the efficiency and reducing the environmental impact of road freight transportation. This paper examines a transitional phase towards a fully unmanned truck fleet, focusing on a platooning approach with a lead driver. The authors develop a novel optimization model for autonomous truck platooning that simultaneously considers platoon formation, scheduling, and routing to minimize costs related to labor and fuel. The model incorporates the possibility of detours, nonlinear fuel savings due to air-drag reduction, and the practical platoon size limit. They present an enhanced column generation method, termed the platoon-generation-and-updating approach, which demonstrates high effectiveness in reducing computational time and complexity. Their numerical analysis, based on the Hong Kong highway network, demonstrates the substantial cost advantages of autonomous truck platooning. It also investigates how platooning efficiency is influenced by various operating factors, including truck fleet size, platoon size restrictions, labor-to-fuel cost ratio, and the strictness of delivery time windows, with practical implications interwoven into the discussion.]]></description>
      <pubDate>Tue, 07 May 2024 09:59:52 GMT</pubDate>
      <guid>https://trid.trb.org/View/2374264</guid>
    </item>
    <item>
      <title>Nested column generation for split pickup vehicle routing problem with time windows and time-dependent demand</title>
      <link>https://trid.trb.org/View/2317513</link>
      <description><![CDATA[This study attempts to solve a split pickup vehicle routing problem with time windows and time-dependent demand. This is a vehicle routing problem in which demand is generated at different constant rates for different customers, and vehicles are allowed to pick up demand during the demand generation process. In this problem, the pickup time determines the quantity of demand that can be picked up, and a partial pickup is permitted during a single visit. The problem is formulated into a mixed-integer nonlinear programming model and a sequence-extended network is designed to represent the relationship between multiple pickups. Because of the interdependences of time, load, and cost in the pricing subproblem, the classic labelling algorithm with weak dominance rules is ineffective, therefore, a nested column generation-based branch-and-price-and-cut algorithm is proposed to tackle the problem. The nested structure allows these trade-offs to be resolved in a lower-level column generation, and it can be applied to other interdependent routing problems. The computational results show that the proposed algorithm is effective in obtaining optimal solutions for small- and medium-scale instances within a reasonable time limit.]]></description>
      <pubDate>Wed, 01 May 2024 09:46:36 GMT</pubDate>
      <guid>https://trid.trb.org/View/2317513</guid>
    </item>
    <item>
      <title>Delay-resistant robust vehicle routing with heterogeneous time windows</title>
      <link>https://trid.trb.org/View/2326668</link>
      <description><![CDATA[The authors consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on which one physical vehicle can serve a customer. This is the main reason why different time windows for different vehicles are of high practical relevance. To ensure that the appointment windows are adhered to as much as possible, the authors introduce a new objective function that penalizes delays. The authors’ novel approach allows them to find solutions that are robust with respect to uncertainties in travel and service times limited by a budget polytope. The authors present a set-partitioning model, the solution of which is based on column generation and employs a labeling algorithm that integrates robustness into the calculations and is adapted to the authors’ problem-specific constraints. In a Monte-Carlo simulation on real-life data, the authors evaluate this method in terms of runtime and solution quality. The authors’ solutions show very good performance, even if the data is more uncertain than assumed for the optimization, incurring only marginal extra travel time compared to a naive deterministic planning scheme.]]></description>
      <pubDate>Fri, 19 Apr 2024 09:38:52 GMT</pubDate>
      <guid>https://trid.trb.org/View/2326668</guid>
    </item>
    <item>
      <title>Adaptive robust electric vehicle routing under energy consumption uncertainty</title>
      <link>https://trid.trb.org/View/2350087</link>
      <description><![CDATA[Electric vehicles (EVs) have been highly favoured as a mode of transportation in recent years. EVs offer numerous benefits over traditional fuel-based vehicles, particularly in terms of the environmental impact. Although electric vehicles offer several advantages, there are certain restrictions that limit their usage. One of the significant issues is the uncertainty in their driving range. The driving range of EVs is closely related to their energy consumption, which is highly affected by exogenous and endogenous factors. Since those factors are unpredictable, uncertainty in EVs’ energy consumption should be considered for efficient operation. This paper proposes a two-stage adaptive robust optimization framework for the electric vehicle routing problem. The objective is to minimize the worst-case energy consumption while guaranteeing that services are delivered at the appointed time windows without battery level deficiency. The authors postulate that EVs can be recharged on route, and the charging amount can be adjusted depending on the circumstances. A column-and-constraint generation based heuristic algorithm, which is coupled with variable neighbourhood search and alternating direction algorithm, is proposed to solve the resulting model. The computational results show the economic efficiency and robustness of the proposed model, and that there is a tradeoff between the total required energy and the risk of failing to satisfy all customers’ demand.]]></description>
      <pubDate>Thu, 18 Apr 2024 17:07:03 GMT</pubDate>
      <guid>https://trid.trb.org/View/2350087</guid>
    </item>
    <item>
      <title>Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility</title>
      <link>https://trid.trb.org/View/2231105</link>
      <description><![CDATA[Motivated by the inbound logistics of a famous automobile manufacturing company, the authors introduce the upward scalable vehicle routing problem (for order pickup) with time windows (USVRPTW), where the pickup from each supplier can be adjusted upward by a certain degree (pickup flexibility) based on the order volume, thus increasing the vehicle utilization and reducing logistics cost. They solve the USVRPTW exactly by a branch-and-price algorithm, where the flexibility affects the pricing problem, leading to the elementary shortest path problem having to consider resource allocation except the resource constraints. The consideration of resource allocation adds many new properties to the shortest path problem, based on which they design a tree search algorithm. They develop a heuristic algorithm based on the bipartite graph to generate initial columns for the column generation (CG) process. The algorithm can also be adopted as an efficient method for solving large-scale problems due to its ability to find near-optimal solutions quickly. They also propose the penalty stabilization method and the drill-down strategy to accelerate CG. Numerical experiments show that their designed branch-and-price algorithm outperforms the commercial solver Gurobi. The efficiency of the tree search algorithm, the heuristic algorithm, and the CG acceleration methods is also verified. Real-data experiments illustrate that the low increase in driving cost can significantly improve vehicle utilization, proving the significance of flexibility. They then provide management insights to reveal that adopting the proposed flexibility mechanism can reduce logistics cost.]]></description>
      <pubDate>Mon, 28 Aug 2023 09:19:09 GMT</pubDate>
      <guid>https://trid.trb.org/View/2231105</guid>
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