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    <title>Transport Research International Documentation (TRID)</title>
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
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    <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>
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      <link>https://trid.trb.org/</link>
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    <item>
      <title>Disruption management in single wagonload transport</title>
      <link>https://trid.trb.org/View/2586409</link>
      <description><![CDATA[In highly utilized rail networks, disruptions can quickly have extensive impact on overall network performance, significantly affecting the reliability and efficiency of transport chains. Dealing immediately with disruptions is important to maintain satisfactory operation level. The authors propose managing disruptions in single wagonload (SWL) transport by optimizing the rerouting and reassigning of railway wagons. The model, DIMENSION, minimizes total delay of railway wagons as well as deviation of train services from the nominal schedule. The model performance is demonstrated on multiple different sized networks derived from real-world German SWL network. The authors conduct computational experiments considering different demands for each network. Results show that the impact of a disruption increases with increasing demand, that the location of a disruption has major influence, and that increasing network size is not necessarily leading to a higher impact of a disruption. Varied network demand results confirm these findings. The proposed model enables to evaluate the impact of disruptions on SWL networks and supports dispatchers to optimize the routing of railway wagons as well as the scheduling of train services. By optimizing network performance during disruptions, DIMENSION helps improving the reliability and quality of transport chains.]]></description>
      <pubDate>Wed, 17 Sep 2025 10:55:40 GMT</pubDate>
      <guid>https://trid.trb.org/View/2586409</guid>
    </item>
    <item>
      <title>Single-stage train formation in railway marshaling stations under an extended railcar-to-track assignment policy</title>
      <link>https://trid.trb.org/View/2483482</link>
      <description><![CDATA[This paper studies a single-stage train formation problem in railway marshaling stations, aiming to efficiently assign railcars to classification tracks with one roll-in and one pull-out operation for ensuring the formation of outbound trains. Assigning railcars to classification tracks by blocks (block-to-track), by outbound trains (train-to-track), and by need (railcar-to-track) are three typical policies widely addressed in the literature. An extended railcar-to-track policy is investigated by combining the first and third policies, where railcars are preferentially assigned to their fixed-use classification tracks through a specified block-to-track scheme and then to other classification tracks if necessary, while re-humping and re-sorting operations are eliminated. The authors formulate the formation problem under this policy as a binary linear programming model with the objective of minimizing the total weighted cost required for train formation, including both the weighted roll-in cost and the weighted pull-out cost. A two-phase decomposition algorithm, which divides the authors' model into a roll-in and a pull-out subproblem, is developed to improve the solving efficiency. For the roll-in subproblem, a novel group-indexed model is constructed to determine a railcar-to-track scheme with minimal total weighted roll-in cost and simplified pull-out cost. For the following pull-out subproblem, the objective is to determine a pull-out scheme that minimizes the total weighted pull-out cost. This subproblem is decomposed further into multiple simplified problems, each of which is formulated into a quadratic assignment model for each outbound train, enabling rapid solving times of this subproblem. Computational results on a set of realistic instances reveal that the authors' algorithm outperforms two benchmark approaches, in which the roll-in subproblem is formulated respectively as a big-M and an arc-indexed model inspired by existing models, and an imitated empirical approach used in practice. The potential superiority of the authors' proposed policy to the three existing policies is also numerically validated.]]></description>
      <pubDate>Mon, 27 Jan 2025 15:39:52 GMT</pubDate>
      <guid>https://trid.trb.org/View/2483482</guid>
    </item>
    <item>
      <title>A Method for the Design of Optimal Locomotive Working Diagrams</title>
      <link>https://trid.trb.org/View/2283277</link>
      <description><![CDATA[The model of assignment problem and the model of minimum rate with maximum flow are principal models for optimizing locomotive working diagrams, however, deficiency occurs when they come to partially double traction. The paper presents a linear integer programming model to solve problems in optimizing locomotive working projects, under paired or unpaired train diagram, single traction, and fully or partially double traction. To predigest solving process and promote practicability, the model is firstly simplified to the model of minimum rate circulation flow and then to the model of minimum rate set flow.]]></description>
      <pubDate>Thu, 17 Oct 2024 09:15:21 GMT</pubDate>
      <guid>https://trid.trb.org/View/2283277</guid>
    </item>
    <item>
      <title>An iterative method for integrated hump sequencing, train makeup, and classification track assignment in railway shunting yard</title>
      <link>https://trid.trb.org/View/2434333</link>
      <description><![CDATA[In a railway shunting yard, the transformation of inbound trains into properly composed outbound trains is a complex task because it involves decisions of multiple operations processes. This study addresses the integrated optimization of hump sequencing, train makeup, and classification track assignment problem in a railway shunting yard. Several key practical yard operation constraints are considered, including train formulation constraints, hump sequencing constraints, and limitations of the maximum number and capacity of classification tracks. By introducing a new representation of block flow, the integrated problem, which adopts the extended single-stage strategy and the train-to-track policy, is formulated as a unified 0-1 integer linear programming model. The objective of the proposed model is to minimize the weighted-sum of the total dwell time of all railcars and the formulation deviation penalties of all outbound trains. Then, an iterative two-phase decomposition approach is developed to reduce the complexity of solving the integrated problem. The first phase aims to explore all feasible humping sequences using a Branch-and-Bound (B&B) algorithm. Each time a new humping sequence is generated in the first phase, the second phase containing a Branch-and-Price (B&P) algorithm is applied to solve the integrated train makeup and classification track assignment problem with the known humping sequence found in the first phase. In addition, greedy heuristics and lower bounding techniques are designed in both phases to improve computational efficiency. Comprehensive experiments are investigated based on a set of real-life instances. The results show that exact approaches provide optimal solutions, whereas heuristic approaches yield satisfactory solutions within a shorter computation time. Moreover, sensitivity analyses on the number of classification tracks and the effects of different deviation penalties are also performed to gain more managerial insights.]]></description>
      <pubDate>Thu, 17 Oct 2024 09:15:19 GMT</pubDate>
      <guid>https://trid.trb.org/View/2434333</guid>
    </item>
    <item>
      <title>The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company</title>
      <link>https://trid.trb.org/View/1841187</link>
      <description><![CDATA[Some of the most important optimization problems faced by railway operators arise from the management of their locomotive fleet. In this paper, the authors study a general version of the locomotive assignment problem encountered at the tactical level by one of the largest railroads in North America: the Canadian National (CN) Railway Company. The authors present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing decisions on each train?s operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it into smaller time windows. Given the difficulty in solving the problem, one of the formulations is enhanced through various refinements, such as constraint relaxations, preprocessing, and fixed cost approximations. The authors thus achieve a significant reduction in the required computational time to solve instances of realistic size. The authors also present two versions of a Benders decomposition?based algorithm to obtain feasible solutions. On average, it allows a reduction of the associated computational time by two hours. Results from an extensive computational study and a case study with data provided by CN confirm the potential benefits of the model and solution approach.]]></description>
      <pubDate>Fri, 21 May 2021 10:55:12 GMT</pubDate>
      <guid>https://trid.trb.org/View/1841187</guid>
    </item>
    <item>
      <title>An MIP-based heuristic solution approach for the locomotive assignment problem focussing on (dis-)connecting processes</title>
      <link>https://trid.trb.org/View/1715704</link>
      <description><![CDATA[Arising from a practical problem in European rail freight transport the authors present a heuristic solution approach that is based on a new generalized mixed integer problem formulation for the Locomotive Assignment Problem. A main focus is on the one hand on the (dis-)connecting processes between cars and locomotives and on the other hand on combining two or more locomotives, i.e., the process of building and busting consists (combination of locomotives). Furthermore, regional limitations for running certain types of locomotives and technical conditions for combining locomotives are taken into account. A generalized solution framework is developed that allows a gradual restricting of the solution space and enables an analysis and comparison of different solution procedures. Testing these for a real-world network as well as several newly generated instances shows that the framework outperforms previous approaches in the literature. Thus a suitable solution method for an application in practice is presented.]]></description>
      <pubDate>Mon, 13 Jul 2020 10:32:58 GMT</pubDate>
      <guid>https://trid.trb.org/View/1715704</guid>
    </item>
    <item>
      <title>A dynamic model for real-time track assignment at railway yards</title>
      <link>https://trid.trb.org/View/1696418</link>
      <description><![CDATA[In this paper, the authors study the real-time train assignment problem (RT-TAP) that arises from the unreliable arrival times of freight trains and the last-minute parking requests at railway yards. In the RT-TAP, the reassignment of trains to the yard is triggered every time a train arrives at the railway yard and needs to be assigned (event-based optimization). After introducing a problem formulation for the RT-TAP problem, the authors prove that RT-TAP is NP-Hard. In particular, the RT-TAP is modeled as a mixed integer program that strives to minimize the total weighted delay of trains. Because of its computational complexity and the time-critical nature of this problem, the authors introduce two real-time solution methods: (a) a problem-specific genetic algorithm (GA), (b) and a first-scheduled first-served (FSFS) heuristic. In small instances, the authors show that the GA returns a globally optimal solution which is identical to the solution of exact optimization methods. In larger problem instances, the heuristic approaches of FSFS and GA are tested at the Waalhaven Zuid railway yard in the Netherlands using two months of operational data. In the experimental results, the GA solutions reduce the average delays by more than 4 min compared to the solutions of the FSFS heuristic.]]></description>
      <pubDate>Fri, 29 May 2020 09:44:09 GMT</pubDate>
      <guid>https://trid.trb.org/View/1696418</guid>
    </item>
    <item>
      <title>Integrated train timetabling and locomotive assignment</title>
      <link>https://trid.trb.org/View/1654835</link>
      <description><![CDATA[Train timetabling and locomotive assignment are often performed separately in a sequential manner. One obvious disadvantage of such hierarchical planning process is that it often results in poor coordination between the train schedule and the locomotive schedule. This paper focuses on modeling and solving an integrated train timetabling and locomotive assignment problem. To solve this integrated problem, the authors first construct a three-dimensional state-space-time network in which a state is used to indicate which train a locomotive is serving. The authors then formulate the problem as a minimum cost multi-commodity network flow problem with incompatible arcs and integer flow restrictions. The authors present a Lagrangian relaxation heuristic for solving this network flow problem. The authors conduct a computational study to test the effectiveness of their Lagrangian relaxation heuristic, compare the performance of their heuristic with that of two benchmark solution methods, and report the benefits obtained by integrating train timetabling and locomotive assignment decisions.]]></description>
      <pubDate>Wed, 18 Dec 2019 15:46:01 GMT</pubDate>
      <guid>https://trid.trb.org/View/1654835</guid>
    </item>
    <item>
      <title>Solving the block-to-train assignment problem using the heuristic approach based on the genetic algorithm and tabu search</title>
      <link>https://trid.trb.org/View/1498163</link>
      <description><![CDATA[After the railroad blocking plan is generated, the block-to-train assignment problem determines which train services to be offered, how many trains of each service to be dispatched (service frequency) and which blocks to be carried by which train services. An integer programming optimization model is defined to solve the block-to-train assignment problem. The model aims to maximize the total cost savings of the whole railroad network compared to the single-block train service plan, where each block is allocated to a direct train service. The objective function includes the service design cost savings, the train operation cost savings, the car-hour consumption savings in the accumulation process, the car-hour consumption savings in the attachment and detachment operations and the waiting car-hour consumption savings. Furthermore, the model is improved to a path-based formulation, which has far fewer decision variables and is easier to solve for real-world problems. A heuristic approach based on the genetic algorithm and tabu search is developed to solve the path-based formulation. The model and approach are tested first in a small network to compare with the optimal solution obtained through the enumeration method and the solution obtained from commercial optimization software. Then the model and approach are applied to a real larger railroad sub-network in China.]]></description>
      <pubDate>Wed, 31 Jan 2018 10:51:08 GMT</pubDate>
      <guid>https://trid.trb.org/View/1498163</guid>
    </item>
    <item>
      <title>Modeling and Optimization for Train-Set Utilization Problem Using a Two-Stage Approach</title>
      <link>https://trid.trb.org/View/1438031</link>
      <description><![CDATA[The utilization efficiency of train-sets (vehicles of high-speed-railway (HSR)) is one of the most important factors influencing the transport capacity of HSR. Therefore, it is imperative to propose a theoretical method to guide efficient train-set utilization in the practical application. In this paper, an integer programming model is established to obtain a high-quality train-set utilization plan. A two-stage approach and a concept of segment are proposed to solve the model. The train graph in the Beijing-Tianjin passenger dedicated line is adopted to illustrate the model application, and a high-quality train-set utilization plan is obtained. Moreover, the comparison between the two-stage approach and the Ant Colony Algorithm (ACA) is conducted to evaluate advancements of the proposed method. The results show that the train-set utilization plan obtained by the two-stage approach is much better in the train-set utilization efficiency as well as the computation time.]]></description>
      <pubDate>Fri, 27 Jan 2017 09:28:47 GMT</pubDate>
      <guid>https://trid.trb.org/View/1438031</guid>
    </item>
    <item>
      <title>Model and Algorithm for Wagons' Placing-In and Taking-Out Problem in Railway Station</title>
      <link>https://trid.trb.org/View/1314567</link>
      <description><![CDATA[Taking the locomotive running time between goods operation sites as weights, wagons' placing-in and taking-out problems can be regarded as a single machine scheduling problem 1| pij | Cij, which can be transformed into a shortest cycle problem of Hamilton graph whose relaxation problem is assignment problem. Firstly, the authors use a Hungarian algorithm to calculate the optimal solution of the assignment problem. Then, the authors provide a Broken-circle and Connection method to find the available order of placing-in and taking-out wagons. The complexity of the algorithm is O(n²). Extensive problems -- such as placing-in and transferring combined or taking-out and transferring combined, placing-in and taking-out combined, placing-in, transferring and taking-out combined -- can also be resolved with the modified model and algorithm. Finally, an instance is given to illustrate the model and the algorithm's reliability and efficiency.]]></description>
      <pubDate>Thu, 31 Jul 2014 09:01:53 GMT</pubDate>
      <guid>https://trid.trb.org/View/1314567</guid>
    </item>
    <item>
      <title>Coordinated Optimization of Wagon Calculating and Taking-Out and Placing-In Wagons Applying Bi-Level Programming Model</title>
      <link>https://trid.trb.org/View/1276311</link>
      <description><![CDATA[Wagon-flow allocation problems and shunting locomotive utilization are two important problems that need to be solved in a station stage plan. Because wagons ready to be taken out from freight yards (special lines) are one of the wagon flow's resources of departure trains, considering the close connection among breaking up operation, marshalling operation, taking-out and placing-in operation, and shunting locomotive activity, takes the shunting locomotive as the core and the breaking up order arrangement of arrival trains, marshalling order arrangement of departure trains, the timing and content of taking-out and placing-in as well as wagon calculating as a whole, and builds the corresponding bi-level programming model.]]></description>
      <pubDate>Mon, 27 Jan 2014 11:27:30 GMT</pubDate>
      <guid>https://trid.trb.org/View/1276311</guid>
    </item>
    <item>
      <title>Locomotive assignment optimization including train delays</title>
      <link>https://trid.trb.org/View/1280112</link>
      <description><![CDATA[Intention– Cyclic locomotive assignment planning is a specific type of organization of locomotive usage, and in fact, it means putting the complete workload to a closed chain, which is repeated periodically. The concept of cyclic locomotive assignment planning type organization in the area of train traction has proven in practice as the best one, but as it is made for in-advance defined timetable and without considering the stochastic nature of the timetable realization process, it leads to incompatibility in using locomotives. Methodology – Methodology defined in this paper contains: research of train delays on the Serbian Railways and Montenegrin Railways networks, analysis of the real system organization of locomotive usage in conditions of train delays, theoretical thesis of solving the problem of optimal cyclic locomotive assignment planning in conditions of train delays, designing of a model with algorithms, preparing the software package, testing the model and program with results, as well as the conclusions drawn from the complete research project. Results– The optimization model of cyclic locomotive assignment planning during the process of making timetable including train delays has been defined. Conclusion –The obtained results have shown as expected, that the larger delays of trains required a larger number of locomotives. However, by using this model it is possible to optimize the required number of locomotives, taking into account the real time delays of trains.]]></description>
      <pubDate>Mon, 23 Dec 2013 11:07:02 GMT</pubDate>
      <guid>https://trid.trb.org/View/1280112</guid>
    </item>
    <item>
      <title>A multi-objective train-scheduling optimization model considering locomotive assignment and segment emission constraints for energy saving</title>
      <link>https://trid.trb.org/View/1253481</link>
      <description><![CDATA[Energy saving and emission reduction for railway systems should not only be studied from a technical perspective but should also be focused on management and economics. On the basis of relevant train-scheduling models for train operation management, in this paper the authors introduce an extended multi-objective train-scheduling optimization model considering locomotive assignment and segment emission constraints for energy saving. The objective of setting up this model is to reduce the energy and emission cost as well as total passenger-time. The decision variables include continuous variables such as train arrival and departure time, and binary variables such as locomotive assignment and segment occupancy. The constraints are concerned with train movement, trip time, headway, and segment emission, etc. To obtain a non-dominated satisfactory solution on these objectives, a fuzzy multi-objective optimization algorithm is employed to solve the model. Finally, a numerical example is performed and used to compare the proposed model with the existing model. The results show that the proposed model can reduce the energy consumption, meet exhausts emission demands effectively by optimal locomotive assignment, and its solution methodology is effective.]]></description>
      <pubDate>Fri, 28 Jun 2013 14:05:14 GMT</pubDate>
      <guid>https://trid.trb.org/View/1253481</guid>
    </item>
    <item>
      <title>Freight Locomotive Rescheduling Algorithm under Disordered Train Operation</title>
      <link>https://trid.trb.org/View/1116701</link>
      <description><![CDATA[When train operations are disrupted, timetables must be adjusted and rolling stock allocation and crew duties are rescheduled. In this paper, the problem of rescheduling locomotive assignment to freight trains after timetable adjustment is discussed. The problem is modeled as an integer programming problem with set-partitioning constraints.  It is solved by column generation technique, which alternatively enumerates candidate locomotive paths and optimizes rescheduling. Numerical experiments of the proposed method are conducted using real data.  Findings from these experiments indicate that this method provides a satisfactory locomotive rescheduling plan in reasonable computing time.  Directions for future research are described.]]></description>
      <pubDate>Wed, 16 May 2012 15:04:43 GMT</pubDate>
      <guid>https://trid.trb.org/View/1116701</guid>
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