Skip to main content
SpringerLink
Log in
SpringerLink
Log in

A Lagrangian Relaxation Based Heuristic for the Urban Transit Crew Scheduling Problem

  • Conference paper
Computer-Aided Transit Scheduling

Part of the book series: Lecture Note in Economics Mathematical Systems ((LNE,volume 308))

Abstract

The transit crew scheduling problem that we consider involves the determination of a set of work days for transit crews that cover all required vehicle movements at minimum cost. This problem is a fundamental one in the transit industry since labor costs predominate in nearly all large transit properties.

Several researchers have approached the transit crew scheduling problem by decomposing it into a shortest path problem and a matching problem. We present an approach based on this decomposition which iterates between the solution of a shortest path problem and the solution of a matching problem. The objective function for the shortest path problem is derived by considering Lagrangian penalties associated with the perfectly matchable subgraph inequalities. This approach is validated on sample problems from the Washington Metropolitan Area Transit Authority (WMATA).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balas, E.; Pulleyblank, W.R.; Perfectly matchable subgraph polytope of a bipartite graph. Networks 13 (1983), 495–516

    Article  Google Scholar 

  2. Ball, M.; Bodin, L.; Dial, R.: A matching based heuristic for scheduling mass transit crews and vehicles. Transportation Science 17 (1982), 4–31

    Article  Google Scholar 

  3. Ball, M.; Bodin, L.; Greenberg, J.: Enhancements to the RUCUS 2 Crew Scheduling System. Computer scheduling of public transport 2. J.M. Rousseau, ed., Elsevier; Amsterdam 1985, 279–293

    Google Scholar 

  4. Benoit, H.: A lagrangian relaxation based heuristic for the urban transit crew scheduling problem. MS Thesis, University of Waterloo, Waterloo, Ontario, Canada 1986

    Google Scholar 

  5. Bodin, L.; Golden, B.; Assad, A.; Ball, M.: Routing and scheduling of vehicles and crews: The state of the art. Computers and Operations Research 10 (1983), 63–211

    Article  Google Scholar 

  6. Carraresi, P.; Gallo, G.: Network models for vehicle and crew scheduling. European Journal of Operations Research 16 (1984), 139–151

    Article  Google Scholar 

  7. Fisher, M.L.: The lagrangian relaxation method for solving integer programming problems. Management Science 27 (1981), 1–18

    Article  Google Scholar 

  8. Hildyard, P.M.; Wallis, H.P.: Advances in computer assisted runcutting in North America. Computer scheduling of public transport. A. Wren, ed., Elsevier, Amsterdam 1981, 183–192.

    Google Scholar 

  9. Lessard, R.; Rousseau, J.M.; Dupuis, D.: HASTUS I: A mathematical programming approach to the bus driver scheduling problem. Computer scheduling of public transport. A. Wren, ed., Elsevier, Amsterdam 1981, 255–267

    Google Scholar 

  10. Luedtke, L.K.: RUCUS II: A review of system capabilities. Computer scheduling of public transport 2. J.M. Rousseau, ed., Elsevier; Amsterdam 1985, 61–116

    Google Scholar 

  11. Rousseau, J.M. (ed.): Computer scheduling of public transport 2, Elsevier Science Publishers, Amsterdam 1985

    Google Scholar 

  12. Rousseau, J.M.; Lessard, R.; Biais, J.: Enhancements to the HASTUS crew scheduling algorithm. Computer scheduling of public transport 2. J.M. Rousseau, ed., Elsevier; Amsterdam 1985, 295–310

    Google Scholar 

  13. Scott, D.: A large scale linear programming approach to the public transport scheduling and costing problem. Computer scheduling of public transport 2. J.M. Rousseau, ed., Elsevier; Amsterdam 1985, 473–491

    Google Scholar 

  14. Wallis, H.: Experiences in computer-assisted scheduling installations in North America. Computer scheduling of public transport 2. J.M. Rousseau, ed., Elsevier; Amsterdam 1985, 11–18

    Google Scholar 

  15. Wren, A. (ed.): Computer Scheduling of Public Transport. Elsevier; Amsterdam 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Business and Management, University of Maryland, College Park, MD, USA

    Michael O. Ball

  2. GIRO Inc., Montréal, Quebec, Canada

    Huguette Benoit-Thompson

Authors
  1. Michael O. Ball
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huguette Benoit-Thompson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. TREUARBEIT Unternehmensberatung GmbH, New-York-Ring 13, D-2000, Hamburg, Germany

    Joachim R. Daduna

  2. Operational Research Unit School of Computer Studies, University of Leeds, Leeds, LS2 9JT, Great Britain

    Anthony Wren (Senior Lecturer) (Senior Lecturer)

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ball, M.O., Benoit-Thompson, H. (1988). A Lagrangian Relaxation Based Heuristic for the Urban Transit Crew Scheduling Problem. In: Daduna, J.R., Wren, A. (eds) Computer-Aided Transit Scheduling. Lecture Note in Economics Mathematical Systems, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85966-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-85966-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19441-5

  • Online ISBN: 978-3-642-85966-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation