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

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 infrastructu...

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Bibliographic Details
Published in:PloS one Vol. 20; no. 5; p. e0322394
Main Authors: Shi, Xin, Zhou, Wenliang, Li, Xiang
Format: Journal Article
Language:English
Published: United States Public Library of Science 27.05.2025
Public Library of Science (PLoS)
Subjects:
Algorithms
Case studies
Computer and Information Sciences
Engineering and Technology
Graph theory
Humans
Integer programming
Linear programming
Management
Mathematical models
Methods
Mixed integer
Models, Theoretical
Nonlinear programming
Operating costs
Optimization
Passenger rail services
Passenger trains
Passengers
Physical Sciences
Planning
Programming, Linear
Railroads
Railway networks
Railways
Research and Analysis Methods
Time dependence
Time Factors
Trains
Transportation planning
China
ISSN:1932-6203, 1932-6203
Online Access:Get full text
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Summary: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.
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Competing Interests: The authors have declared that no competing interests exist.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0322394