Fewer Trains for Better Timetables: The Price of Fixed Line Frequencies in the Passenger-Oriented Timetabling Problem

Authors Pedro José Correia Duarte , Marie Schmidt , Dennis Huisman , Lucas P. Veelenturf

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Pedro José Correia Duarte
  • Econometric Institute, Erasmus Center for Optimization in Public Transport (ECOPT), Erasmus University Rotterdam, The Netherlands
Marie Schmidt
  • Institute of Computer Science, Faculty of Mathematics and Computer Science, Universität Würzburg, Germany
Dennis Huisman
  • Econometric Institute, Erasmus Center for Optimization in Public Transport (ECOPT), Erasmus University Rotterdam, The Netherlands
  • Process quality and Innovation, Netherlands Railways, Utrecht, The Netherlands
Lucas P. Veelenturf
  • Department of Technology and Operations Management, Rotterdam School of Management, Erasmus University, Rotterdam, The Netherlands

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Pedro José Correia Duarte, Marie Schmidt, Dennis Huisman, and Lucas P. Veelenturf. Fewer Trains for Better Timetables: The Price of Fixed Line Frequencies in the Passenger-Oriented Timetabling Problem. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


This paper introduces the Passenger-Oriented Timetabling problem with flexible frequencies (POT-flex) in the context of railway planning problems. POT-flex aims at creating feasible railway timetables minimising total perceived passenger travel time. The contribution of the POT-flex lies in its relaxation of the generally adopted assumption that line frequencies should be a fixed part of the input. Instead, we consider flexible line frequencies, encompassing a minimum and maximum frequency per line, allowing the timetabling model to decide on optimal line frequencies to obtain better solutions using fewer train services per line. We develop a mixed-integer programming formulation for POT-flex based on the Passenger-Oriented Timetabling (POT) formulation of [Polinder et al., 2021] and compare the performance of the new formulation against the POT formulation on three instances. We find that POT-flex allows to find feasible timetables in instances containing bottlenecks, and show improvements of up to 2% on the largest instance tested. These improvements highlight the cost that fixed line frequencies can have on timetabling.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • PESP
  • Passenger Oriented Timetabling
  • Perceived Travel Time


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