A lagrangian relaxation method for crew and vehicle rescheduling of railway passenger transportation and its application

Tatsuhiro Sato, Tomoe Tomiyama, Toyohisa Morita, Tomohiro Murata

Research output: Contribution to journalArticle

2 Citations (Scopus)


We propose a method for solving the crew rescheduling problem (CRP) and the vehicle rescheduling problem (VRP) based on the Lagrangian relaxation method. The CRP/VRP is formulated as an integer programming problem on the basis of a network flow modeling approach from which a Lagrangian relaxation problem is constructed by relaxing the constraint that links multiple resources. Using two procedures that generate the upper and lower bounds of the primal problem, both of which utilize an efficient shortest path algorithm for the directed acyclic graph (DAG), the proposed method gradually improves the gap between the upper and lower bounds while updating Lagrangian multipliers. Experimental results of real-world vehicle rescheduling data from Japanese railway lines indicated that the proposed method generated feasible solutions that were confirmed to be fairly close to the optimal solutions according to the gap between the upper and lower bounds, and also clarified the quality of the other method's solution by using the gap, which could lead to streamlining and sophisticating real-world rescheduling related activities.

Original languageEnglish
Pages (from-to)260-268
Number of pages9
JournalIEEJ Transactions on Electronics, Information and Systems
Issue number2
Publication statusPublished - 2012



  • Crew/vehicle rescheduling
  • Integer programming
  • Lagrangian relaxation method
  • Network flow model
  • Railway train operation
  • Shortest path algorithm

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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