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A mixed-integer linear programming method for time-dependent line planning in passenger railway systems

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  • Xin Shi
  • Wenliang Zhou
  • Xiang Li

Abstract

This paper addresses a line planning problem (LPP) that simultaneously optimizes both train and passenger times in passenger railway systems, considering time-dependent origin-destination-period demand and passenger train choice. The problem is clearly and flexibly modeled in a physical infrastructure-based directed graph, which efficiently integrates the train operation choice and the passenger train choice. The problem is first formulated as a mixed-integer, non-concave, and non-linear programming model aimed at minimizing both the total operating cost of trains and the total travel cost of passengers. To solve the problem, an extended time-dimension method is proposed to transform the non-concave and non-linear model into a mixed-integer linear programming (MILP) model that can be solved using a commercial solver. Additionally, a set of simplification strategies is introduced to reduce the computational complexity while ensuring the global optimality of the linear model. A case study of a busy Chinese railway line demonstrates that the optimized time-dependent line plan enhances operational efficiency and accommodates the diversified travel preferences driven by time-dependent demand.

Suggested Citation

  • Xin Shi & Wenliang Zhou & Xiang Li, 2025. "A mixed-integer linear programming method for time-dependent line planning in passenger railway systems," PLOS ONE, Public Library of Science, vol. 20(5), pages 1-32, May.
    • Handle: RePEc:plo:pone00:0322394
    DOI: 10.1371/journal.pone.0322394
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    References listed on IDEAS

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    1. Ralf Borndörfer & Martin Grötschel & Marc E. Pfetsch, 2007. "A Column-Generation Approach to Line Planning in Public Transport," Transportation Science, INFORMS, vol. 41(1), pages 123-132, February.
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