Benders Decomposition for Passenger-Oriented Train Timetabling with Hybrid Periodicity

TL;DR

The paper addresses a complex problem of hybrid periodic train timetabling by integrating periodic and aperiodic operations with rolling stock circulation and passenger routing. It introduces a time-space network representation and an arc-path mathematical formulation, solved via a decomposition framework that combines Benders decomposition with column generation, augmented by preprocessing and cut-strengthening techniques. A variant fixing routes for a subset of passenger groups (PSR) is proposed to improve scalability on large instances. Numerical experiments on toy and real-world networks (e.g., Lower Saxony) demonstrate that hybrid periodicity can reduce passenger travel costs and that the BD+CG approach is effective and scalable with appropriate acceleration. The work provides a practical, passenger-oriented methodology for designing flexible, executable timetables under capacity and budget constraints, with potential extensions to deeper RSU coupling and multi-day horizons.

Abstract

Periodic timetables are widely adopted in passenger railway operations due to their regular service patterns and well-coordinated train connections. However, fluctuations in passenger demand require varying train services across different periods, necessitating adjustments to the periodic timetable. This study addresses a hybrid periodic train timetabling problem, which enhances the flexibility and demand responsiveness of a given periodic timetable through schedule adjustments and aperiodic train insertions, taking into account the rolling stock circulation. Since timetable modifications may affect initial passenger routes, passenger routing is incorporated into the problem to guide planning decisions towards a passenger-oriented objective. Using a time-space network representation, the problem is formulated as a dynamic railway service network design model with resource constraints. To handle the complexity of real-world instances, we propose a decomposition-based algorithm integrating Benders decomposition and column generation, enhanced with multiple preprocessing and accelerating techniques. Numerical experiments demonstrate the effectiveness of the algorithm and highlight the advantage of hybrid periodic timetables in reducing passenger travel costs.

Figures (8)

• Figure 1: Example of the time-space network representation.
• Figure 2: Experimental results of the stop-skipping technique of extra train services
• Figure 3: Experiment results with different periodicity levels and time windows
• Figure 4: Illustration of transfer missing phenomenon
• Figure 5: Illustration of different minimum headway times