Public Transport

, Volume 9, Issue 1–2, pp 33–53 | Cite as

The railway line frequency and size setting problem

  • Alicia De-Los-Santos
  • Gilbert Laporte
  • Juan A. Mesa
  • Federico Perea
Original Paper


The problem studied in this paper takes as input data a set of lines forming a railway network, and an origin–destination (OD) matrix. The OD pairs may use either the railway network or an alternative transportation mode. The objective is to determine the frequency/headway of each line as well as its number of carriages, so that the net profit of the railway network is maximized. We propose a mixed integer non-linear programming formulation for this problem. Because of the computational intractability of this model, we develop four algorithms: a mixed integer linear programming (MIP) model, a MIP-based iterative algorithm, a shortest-path based algorithm, and a local search. These four algorithms are tested and compared over a set of randomly generated instances. An application over a case study shows that only the local search heuristic is capable of dealing with large instances.


Railway line planning Mathematical programming Heuristics 



This research was partly funded by the Canadian Natural Sciences and Engineering Research Council under Grant 2015-06189, by the Ministerio de Economía y Competitividad (Spain)/FEDER under projects MTM2012-37048, MTM2015-67706-P and DPI2012-36243-C02-01, and by Junta de Andalucía (Spain)/FEDER under excellence project P10-FQM-5849. Part of this research was done while Federico Perea was enjoying a research visit to CIRRELT, funded by the Universitat Politècnica de València, under program PAID-00-15. This support is gratefully acknowledged. Thanks are due to the referees for their valuable comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Departamento de Estadística, Econometría, Investigación OperativaOrganización de Empresas y Economía Aplicada, Universidad de CórdobaCórdobaSpain
  2. 2.Departamento de Matemática Aplicada IIUniversidad de SevillaSevilleSpain
  3. 3.CIRRELT and Canada Research Chair in Distribution ManagementMontrealCanada
  4. 4.Instituto Tecnológico de InformáticaUniversitat Politècnica de ValènciaValenciaSpain

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