Comprehensive Optimisation Study of Train Formation Plans at Loading Stations Considering Multi-Shipment Direct Trains
Downloads
This paper analyses the situation where the car flows at loading stations are small and concentrated, and based on existing literature, proposes an optimisation model for multi-modal transportation in loading station train formation plans. This model transports small car flows by adding two types of multi-shipment direct trains. Based on this, an optimised train formation plan model for loading stations, considering multi-shipment direct trains, was designed. This model is a nonlinear 0-1 integer programming model that satisfies constraints such as the uniqueness of car flow organisation, reclassification capacity constraints at technical stations, conditions for operating direct trains from the loading station and small car flow organisation constraints. The objective is to minimise the costs associated with loading, unloading and reclassification during transportation. To enable the use of commercial solvers for solving the model, linearisation techniques were applied to convert the model into a linear form. Finally, the model is solved using Gurobi, with the example of the Northern Passage of Xinjiang Coal Transportation. According to the results, 6 multi-shipment direct trains are organised from the loading station to the unloading station, 3 multi-shipment direct trains are sent to the technical station en route, 2 groups of car flows are sent to the first technical station by local trains, and 10 other groups of car flows are organised into direct trains from the loading station to the technical station. The total cost is 28,922.6 train hours. Additionally, comparing the experimental results with the scheme that only uses local or detachable trains to transport small car flows demonstrates the effectiveness of the proposed model, As a result, the total train-hour consumption was reduced by 9.273% compared to the formation plan without considering multi-shipment direct trains. The utilisation rates of reclassification capacity at the two technical stations decreased by 100% and 25.57%, respectively. The case study fully demonstrates the effectiveness of the proposed model.
Downloads
Bodin LD, et al. A model for the blocking of Trains. Transportation Research Part B: Methodological. 1980;14(1–2):115–20. DOI: 10.1016/0191-2615(80)90037-5.
Haghani AE. Formulation and solution of a combined train routing and makeup, and empty car distribution model. Transportation Research Part B: Methodological. 1989;23(6):433-452. DOI: 10.1016/0191-2615(89)90043-x.
Lin BL, et al. Optimizing the freight train connection service network of a large-scale rail system. Transportation Research Part B: Methodological. 2012;46(5):649-667. DOI: 10.1016/j.trb.2011.12.003.
Keaton MH. Designing optimal railroad operating plans: Lagrangian relaxation and heuristic approaches. Transportation Research Part B: Methodological. 1989;23(6):415-431. DOI: 10.1016/0191-2615(89)90042-8.
Keaton MH. Designing railroad operating plans: A dual adjustment method for implementing Lagrangian relaxation. Transportation science. 1992;26(4):263-279. DOI: 10.1287/trsc.26.4.263.
Badetskii A, et al. Improving the stability of the train formation plan to uneven operational work. Transportation Research Procedia. 2021;54:559-567. DOI: 10.1016/j.trpro.2021.02.108.
Liang D, et al. Study on the theory and model of the optimal train formation plan of multi-block trains at technical service stations. Journal of the China Railway Society. 2006;28(3):1-5. DOI: 10.3321/j.issn:1001-8360.2006.03.001.
Xiao J, et al. Solving the train formation plan network problem of the single-block train and two-block train using a hybrid algorithm of genetic algorithm and tabu search. Transportation Research Part C: Emerging Technologies. 2018;86:124-146. DOI: 10.1016/j.trc.2017.10.006.
Lin BL, et al. The optimal model of the direct train formation plan for loading area. China Railway Science. 1995;16(2):117-120.
Cao XM, et al. Optimization of direct freight train service in the loading place. Journal of the China Railway Society. 2006;28(4):6-11. DOI: 10.3321/j.issn:1001-8360.2006.04.002.
Ji LJ, et al. Study on the optimization of car flow organization for loading area based on logistics cost. Journal of The China Railway Society. 2009:1-6. DOI: 10.3969/j.issn.1001-8360.2009.02.001.
Ma B, et al. Research on the organization of direct trains from loading stations in railway transport. Railway Transportation and Economics. 2020;(01):19-23. DOI: 10.16668/j.cnki.issn.1003-1421.2020.01.04.
Long W, et al. Synthetically optimizing direct train services from loading area technical yards and within local sections. Journal of Transportation Systems Engineering and Information Technology. 2013;13(5):127. DOI: 10.16097/j.cnki.1009-6744.2013.05.013.
Jie J. Research on the matching technology of direct train formation and heavy load technical direct train formation [D]. Beijing Jiaotong University. 2010.
Zhao Y, et al. The multi-shipment train formation optimization problem along the ordered rail stations based on collection delay. IEEE Access. 2019;7:75935-75948. DOI: 10.1109/ACCESS.2019.2921619.
Ahuja RK, et al. Solving real-life railroad blocking problems. Interfaces. 2007;37(5):404-419. DOI: 10.1287/inte.1070.0295.
Belošević I, et al. Variable neighborhood search for multistage train classification at strategic planning level. Computer‐Aided Civil and Infrastructure Engineering. 2018;33(3):220-242. DOI: 10.1111/mice.12304.
Ruf M, et al. Adaptive large neighborhood search for integrated planning in railroad classification yards. Transportation Research Part B: Methodological. 2021;150:26-51. DOI: 10.1016/j.trb.2021.05.012.
Zhang S, et al. Single-stage train formation in railway marshaling stations under an extended railcar-to-track assignment policy. Transportation Research Part C: Emerging Technologies. 2025;171:104972. DOI: 10.1016/j.trc.2024.104972.
Yaghini M, et al. Solving train formation problem using simulated annealing algorithm in a simplex framework. Journal of Advanced Transportation. 2014;48(5):402-416. DOI: 10.1002/atr.1183.
Carey M. A model and strategy for train pathing with choice of lines, platforms, and routes. Transportation Research Part B: Methodological. 1994;28(5):333-353. DOI: 10.1016/0191-2615(94)90033-7.
Li H, et al. Research on optimization algorithm of single-block train formation plan of technical station. International Journal of Computers Communications & Control. 2023;18(5). DOI: 10.15837/ijccc.2023.5.5255.
Qi L. Comprehensive optimization of direct loading station trains and technical direct train formation plans. Master’s Thesis, Beijing Jiaotong University. 2020. DOI: 10.26944/d.cnki.gbfju.2020.000968.
Chen M, et al. A self-adaptive fast fireworks algorithm for effective large-scale optimization. 2023;80. DOI: 10.1016/j.swevo.2023.101314.
Dulebenets MA. An adaptive polyploid memetic algorithm for scheduling trucks at a cross-docking terminal. Information Sciences. 2021;565:390-421. DOI: 10.1016/j.ins.2021.02.039.
Li B, et al. A holistic optimization-based approach for sustainable selection of level crossings for closure with safety, economic, and environmental considerations. Reliability Engineering & System Safety. 2024;249:110197. DOI: 10.1016/j.ress.2024.110197.
Dulebenets MA. A diffused memetic optimizer for reactive berth allocation and scheduling at marine container terminals in response to disruptions. Swarm Evol. Comput. 2023;80(2023):101334. DOI: 10.1016/j.swevo.2023.101334.
Copyright (c) 2026 Chao HE, Hai jun LI, Ru Hu GAO
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
