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Robust Integrated Model for Traffic Routing Optimization and Train Formation Plan with Yard Capacity Constraints and Demand Uncertainty

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Abstract

The optimal planning of shipments with optimal traffic routing and train service provision subject to capacity limits is a major problem in rail transport. These services are the subject of the Train Formation Plan (TFP) problem, which concerns choosing how to rearrange and redistribute cars at different stations or yards. Another key issue is how to choose the right routes for trains from among the variety of paths on which they can travel between two points, which is the subject of the Traffic Routing (TR) problem. Integrating these two problems can provide better train formation and routing results. Other important issues in this area include the capacity of rail yards and the possibility of uncertainty in decision parameters like demand, which needs to be considered to have a realistic model. This article presents an integrated TFP-TR model with yard capacity constraints and demand uncertainty. The problem was formulated as a non-linear model and then the robust formulation of the model was developed using Bertsimas and Sim’s method. The objective was defined as the minimization of the cost. The solution approach was validated by applying the model to an example designed according to Chinese rail transportation network.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

TFP:

Train Formation Plan

TR:

Traffic Routing

MIP:

Mixed Integer Programming

LR:

Lagrangian relaxation

SA:

Simulated Annealing

MILP:

Mixed-Integer Linear Programming

References

  1. Bodin, L.D., Golden, B.L., Schuster, A.D., Romig, W.: A model for the blocking of trains. Transport. Res. B Meth. 14, 115–120 (1980). https://doi.org/10.1016/0191-2615(80)90037-5

    Article  MathSciNet  Google Scholar 

  2. Assad, A.: Analysis of rail classification policies. INFOR: Information Systems and Operational Research 21, 4:293–314 (1983)

  3. Dyke, C.D.: The automated blocking model: a practical approach to freight railroad blocking plan development. Transp. Res. Forum 27, 116–121 (1986)

    Google Scholar 

  4. Dyke, C.D.: Dynamic management of railroad blocking plans. Transp. Res. Forum 29, 149–152 (1988)

    Google Scholar 

  5. Newton, H.N.: Network design under budget constraints with application to the railroad blocking problem. Auburn University (1996)

  6. Newton, H., Barnhart, C., Vance, P.: constructing railroad blocking plans to minimize handling costs. Transport. Sci. 32, 330–345 (1998). https://doi.org/10.1287/trsc.32.4.330

    Article  Google Scholar 

  7. Barnhart, H., **, P.H.V.: Railroad blocking: a network design application. Oper. Res. 48, 603–614 (2000). https://doi.org/10.1287/opre.48.4.603.12416

    Article  Google Scholar 

  8. Goli, A., et al.: Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry. Comput. Ind. Eng. 137, 106090 (2019)

    Article  Google Scholar 

  9. Ahuja, R.K., Cunha, C.B., Şahin, G.: Network models in railroad planning and scheduling Tutor. Oper. Res. 1(54), 101 (2005). https://doi.org/10.1287/educ.1053.0013

    Article  Google Scholar 

  10. Ahuja, R.K., Jha, K.C., Liu, J.: solving real-life railroad blocking problems. Interfaces Provid. 37, 404–419 (2007). https://doi.org/10.1287/inte.1070.0295

    Article  Google Scholar 

  11. Yaghini, M., Foroughi, A., Nadjari, B.: Solving railroad blocking problem using ant colony optimization algorithm. Appl. Math. Model. 35, 5579–5591 (2011). https://doi.org/10.1016/j.apm.2011.05.018

    Article  MathSciNet  Google Scholar 

  12. Yaghini, M., Momeni, M., Sarmadi, M., Seyedabadi, M., Khoshraftar, M.: A fuzzy railroad blocking model with genetic algorithm solution approach for Iranian railways. Appl. Math. Model. 39, 6114–6125 (2011). https://doi.org/10.1016/j.apm.2015.01.052

    Article  MathSciNet  Google Scholar 

  13. Chen, C., Dollevoet, T., Zhao, J.: One-block train formation in large-scale railway networks: An exact model and a tree-based decomposition algorithm. Transportation Research Part B:Methodological 118, 1–30 (2018)

    Article  Google Scholar 

  14. Yaghini, M., Momeni, M., Sarmadi, M.: An improved local branching approach for train formation planning. Appl. Math. Model. 37(4), 2300–2307 (2013)

    Article  MathSciNet  Google Scholar 

  15. Borndörfer, R., Klug, T., Schlechte, T., Fügenschuh, A., Schang, T., Schülldorf, H.: The freight train routing problem for congested railway networks with mixed traffic. Transp. Sci. 50(2), 408–423 (2016)

    Article  Google Scholar 

  16. Wang, Y., Song, R., He, S., Song, Z., Chi, J.: Optimizing Train Routing Problem in a Multistation High-Speed Railway Hub by a Lagrangian Relaxation Approach. IEEE Access 10, 61992–62010 (2022)

    Article  Google Scholar 

  17. D’Ariano, A.: Innovative decision support system for railway traffic control. IEEE Intell. Transp. Syst. Mag. 1(4), 8–16 (2009)

    Article  Google Scholar 

  18. Lin, B., Zhao, Y., Lin, R., Liu, C.: Integrating traffic routing optimization and train formation plan using simulated annealing algorithm. Appl. Math. Model. 93, 811–830 (2021)

    Article  MathSciNet  Google Scholar 

  19. Lin, B., Wang, Z., Zhao, Y.: A Train Formation Plan with Elastic Capacity for Large-Scale Rail Networks. ar**v:2111.03473 (2021). https://doi.org/10.48550/ar**v.2111.03473

  20. Lin, B.: Integrating car path optimization with train formation plan: A non-linear binary programming model and simulated annealing based heuristics. ar**v:1707.08326 (2017). https://doi.org/10.48550/ar**v.1707.08326

  21. Yaghini, M., Momeni, M., Sarmadi, M.: Solving train formation problem using simulated annealing algorithm in a simplex framework. J. Adv. Transport. 48, 402–416 (2014). https://doi.org/10.1002/atr.1183

    Article  Google Scholar 

  22. Hasany, R., Shafahi, Y.: Two-stage stochastic programming for the railroad blocking problem with uncertain demand and supply resources. Comput. Ind. Eng. 106, 275–286 (2017). https://doi.org/10.1016/j.cie.2017.02.014

    Article  Google Scholar 

  23. Hasany, R., Shafahi, Y.: Two-stage stochastic programming for the railroad blocking problem with uncertain demand and supply resources. Comput. Ind. Eng. 106, 275–286 (2017). https://doi.org/10.1016/j.cie.2017.02.014

    Article  Google Scholar 

  24. Yaghini, M., Momeni, M., Sarmadi, M.: A hybrid solution method for fuzzy train formation planning. Appl. Soft Comput. 31, 257–265 (2015)

    Article  Google Scholar 

  25. Noruzi, M., et al.: A Robust Optimization Model for Multi-Period Railway Network Design Problem Considering Economic Aspects and Environmental Impact. Sustainability 15(6), 5022 (2023)

    Article  Google Scholar 

  26. Lin, B.L., Wang, Z.M., Ji, L.J., Tian, Y.M., Zhou, G.Q.: Optimizing the freight train connection service network of a large-scale rail system. Transport. Res. B Meth. 46, 649–667 (2012). https://doi.org/10.1016/j.trb.2011.12.003

    Article  Google Scholar 

  27. Lin, B.L., Wang, Z.M., Ji, L.J., Tian, Y.M., Zhou, G.Q.: Optimizing the freight train connection service network of a large-scale rail system. Transport. Res. B Meth. 46, 649–667 (2012). https://doi.org/10.1016/j.trb.2011.12.003

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the Faculty of Industrial Engineering, Isfahan University of Technology.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Isfahan University of Technology, Isfahan, Islamic Republic of Iran

    Shima Aghaee, Mehdi Alinaghian & Mohammad Aghaee

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  1. Shima Aghaee
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  2. Mehdi Alinaghian
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  3. Mohammad Aghaee
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Contributions

S.A and Mo.A Conceived and designed the analysis, contributes data or analysis tools, performed the analysis and wrote the paper. Me.a verified the muanscript.

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Correspondence to Shima Aghaee.

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Aghaee, S., Alinaghian, M. & Aghaee, M. Robust Integrated Model for Traffic Routing Optimization and Train Formation Plan with Yard Capacity Constraints and Demand Uncertainty. Int. J. ITS Res. (2024). https://doi.org/10.1007/s13177-024-00406-3

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  • DOI: https://doi.org/10.1007/s13177-024-00406-3

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