Optimising the travel time of a line plan

Simon Henry Bull, Jesper Larsen*, Richard Martin Lusby, Natalia Jurjevna Rezanova

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

96 Downloads (Pure)


The line planning problem that arises in the planning of a passenger railway involves selecting a number of lines from a potential pool to provide sufficient passenger capacity, meeting operational requirements, while optimising some measure of line quality. We model, and solve, the problem of minimising the average passenger system time, including frequency-dependent estimates for switching between lines in collaboration with Danish State Railways (DSB). We present a multi-commodity flow formulation for the problem of freely routing passengers, coupled to discrete line-frequency decisions selecting lines from a predefined pool. The performance of the developed methodology is analysed on instances taken from the suburban commuter network, DSB S-tog, in Copenhagen, Denmark. We show that the proposed approach yields line plans that are superior from both an operator and a passenger perspective to line plans that have been implemented in practice.
Original languageEnglish
Issue number3
Pages (from-to)225-259
Publication statusPublished - 2019


  • Passenger railway optimisation
  • Line planning
  • Mixed integer programming Mathematics Subj


Dive into the research topics of 'Optimising the travel time of a line plan'. Together they form a unique fingerprint.

Cite this