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The average load of 16 express train arcs in the system is For ordinary train arcs, because they also transport other bulk non-value-added car flows, their workloads are not discussed here. The flow pattern of each arc i. In Fig 4 , we select two express trains and two ordinary trains for illustration.
The express train X shown by red arcs in Fig 4 originates at station B and ends at station Y In this paper, a car-to-train assignment model for rail express cargos is proposed. According to the characteristics of high value-added goods, the transportation due date constraint is added to the model, considering both the transportation time on the arcs and the transfer time between the arcs.
In addition, the arc capacity constraint and flow balance constraint are considered. Moreover, linearization techniques are used to make the model linear so that it can be directly solved by a standard optimization solver. Finally, an illustrative case study is carried out based on the Beijing-Guangzhou Railway Line, which is one of the busiest railway lines in China.
The example consists of 13 nodes and 43 arcs, and we consider the northward direction.
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The detailed car-to-train assignment plan is obtained based on the analysis of the optimal solution. The results indicate that the model has a certain significance in real-life application to the rail express cargos assignment problem. Note that it is assumed that the train operation plan, mainly the scheduled train services network, is given, which is developed manually in practice without any optimization-based approach.
In this case, the resulting car-to-train assignment plan can serve as a solid aid in improving the quality of train operation planning. In the long term, researchers can focus on the joint optimization of the train operation plan and the car-to-train assignment plan. In addition, the railway network and the cargo volume in China are huge. For such a large-scale network and data, the efficiency of the algorithm in this paper is far from enough for practical application, so the solution method of the model needs to be further improved.
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We would like to thank Mr. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. National Center for Biotechnology Information , U.
PLoS One. Published online Oct Yong-Hong Kuo, Editor. Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist. Received Apr 5; Accepted Sep This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract A freight train service network generally involves two categories of trains: unscheduled trains, whose operating frequencies fluctuate with the freight demand, and scheduled trains, which are operated based on regular timetables similar to passenger trains. Introduction In recent years, the competition between railway and highway transportation has become increasingly intense, especially for the long-distance transportation of high-value freight. Related work Generally, the core of the car-to-train assignment problem involves the two consolidation processes: the car-to-block assignment and the block-to-train assignment.
The contributions of this work to the existing research literature can be summarized as follows: The operating frequencies of the unscheduled trains fluctuate with the freight demand, while the scheduled trains are operated based on regular timetables similar to the passenger trains; this paper coordinately considers the train service network that involves both the unscheduled trains and the scheduled trains.
Problem descriptions In this paper, a car is a rail vehicle or a wagon used as loading units for measuring the volume of shipments, while the train is consisted of multiple cars with the same or different destinations. Open in a separate window. Fig 1. Mathematical model This section aims to provide a mathematical description for the rail express cargo car-to-train assignment problem. To facilitate the model formulation, we make the following assumptions throughout this paper: Each city has at least one railway station, and different stations including marshalling stations and logistics centers in a city can be connected by local train services.
Proportion of the volume of the g th shipment that is able to be transported; x g m : Binary variables. Linearization There exist several nonlinear constraints in the original model, including constraints 2 , 3 , 5 and 6. Fig 2. Fig 3. Table 1 Information on the shipments. Table 2 Information on the train services. Wuhan North hr 8. Table 4 Transfer time between arc m and arc n. Computational results and analysis We solve the model of the car-to-train assignment problem by Gurobi 7. Table 5 Results of the car-to-train assignment. Table 6 Workloads of the express train arcs.
Fig 4. Conclusions In this paper, a car-to-train assignment model for rail express cargos is proposed. Acknowledgments We would like to thank Mr. Data Availability All relevant data are within the paper. References 1. Flow assignment model for quantitative analysis of diverting bulk freight from road to railway. Plos One. A model for the blocking of trains. Transportation Research Part B: Methodological.
Train planning in a fragmented railway: a British perspective
Constructing railroad blocking plans to minimize handling costs. Transportation Science. Railroad blocking a network design application. Operations Research. Solving railroad blocking problem using ant colony optimization algorithm. Applied Mathematical Modelling.
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Solving real-life railroad blocking problems. Modeling the railway network design problem: A novel approach to considering carbon emissions reduction. Thomet MA. Routing and scheduling temporal and heterogeneous freight car traffic on rail networks. New approaches for solving the block-to-train assignment problem. Xiao J, Lin BL. Comprehensive optimization of the one-block and two-block train formation plan. Solving the block-to-train assignment problem using the heuristic approach based on the genetic algorithm and tabu search. Transportation Research Part B : Methodological. Hwang T, Ouyang Y.
Published online in Articles in Advance 31 Mar Keaton MH. Haghani AE. Rail freight transportation: A review of recent optimization models for train routing and empty car distribution. Formulation and solution of a combined train routing and makeup, and empty car distribution model. Optimizing the freight train connection service network of a large-scale rail system.
Despite some initial setbacks, by the project was being hailed as an unexpected success, spurring record passenger numbers and substantially contributing to the growth of regional Victorian economies. In the years following the completion of the RFR program, a number of further large-scale investments in the regional rail network were proposed and completed. Some of these projects are directly attributable to the problems of the patronage growth which resulted from the RFR upgrades; others focus on similar aims to those of the original project, such as improving travel times and reliability.
Additionally, from , intermediate carriages were ordered, creating a fleet of 3-car sets in place of the original 2-car trains.
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