Skip to main content

Advertisement

Springer Nature Link
Log in

The vehicle routing problem with coupled time windows

  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

In this article we introduce the vehicle routing problem with coupled time windows (VRPCTW), which is an extension of the vehicle routing problem with time windows (VRPTW), where additional coupling constraints on the time windows are imposed. VRPCTW is applied to model a real-world planning problem concerning the integrated optimization of school starting times and public bus services. A mixed-integer programming formulation for the VRPCTW within this context is given. It is solved using a new meta-heuristic that combines classical construction aspects with mixed-integer preprocessing techniques, and improving hit-and-run, a randomized search strategy from global optimization. Solutions for several randomly generated and real-world instances are presented.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anthony R.N. (1964), Framework for analysis. Management Services (March–April): 18–24.

  2. Bar-Yehuda R., Rawitz D. (2001), Efficient algorithms for integer programs with two variables per constraint. Algorithmica 29(4), 595–609.

    Article  Google Scholar 

  3. Bell M.G.H. (1983), The Estimation of an Origin-Destination Matrix from Traffic Counts. Transportation Science 17(2): 198–217.

    Google Scholar 

  4. Bodin L., Berman L. (1979), Routing and Scheduling of School Buses by Computer. Transportation Science 13(2), 113–129.

    Google Scholar 

  5. Borndörfer R., Grötschel M., Löbel A. (2003), Duty Scheduling in Public Transit. Technical Report 01-02, Zuse Institut, Berlin.

    Google Scholar 

  6. Borndörfer R., Grötschel M., Pfetsch M. (2005), Path-Based Model for Line Planning in Public Transport. Technical Report 05-18, Zuse Institut, Berlin.

    Google Scholar 

  7. Borndörfer R., Löbel A., Weider S. (2004), A Bundle Method for Integrated Multi-Depot Vehicle and Crew Scheduling in Public Transit. Technical Report 04-14, Zuse Institut, Berlin.

    Google Scholar 

  8. Bowerman R.L., Hall G.B., Calamai P.H. (1995), A Multi-Objective Optimisation Approach to School Bus Routing Problems. Transp. Research A 28(5), 107–123.

    Google Scholar 

  9. Braca J., Bramel J., Posner B., Simchi-Levi D. (1997), A Computerized Approach to the New York City School Bus Routing Problem. IIE Transactions 29, 693–702.

    Article  Google Scholar 

  10. Bussieck M.R., Kreuzer P., Zimmermann U.T. (1996), Optimal lines for railway systems. European J. Oper. Res. 96, 54–63.

    Article  Google Scholar 

  11. Bussieck M.R., Winter T., Zimmermann U.T. (1997), Discrete Optimization in Public Rail Transport. Mathematical Programming 79, 415–444.

    Article  Google Scholar 

  12. Carey M., Hendrickson C., Siddharthan K. (1981), A Method for Direct Estimation of Origin Destination Trip Matrices. Transportation Science 15(1): 32–49.

    Google Scholar 

  13. Claessens M.T., van Dijk N.M., Zwaneveld P.J. (1995), Cost Optimal Allocation of Rail Passenger Lines. European Journal Operation Research 110(3), 474–489.

    Article  Google Scholar 

  14. Clarke G., Wright J. (1964), Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12, 568–581.

    Google Scholar 

  15. Corberan A., Fernandez E., Laguna M., Marti R. (2000), Heuristic Solutions to the Problem of Routing School Buses with Multiple Objectives. Technical Report TR08-2000, Dep. of Statistics and OR, University of Valencia, Spain.

    Google Scholar 

  16. Cordeau J.-F., Desaulniers G., Desrosiers J., Solomon M.M., Soumis F. (2002), VRP with time windows. In: Toth P., Vigo D. (eds.), The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, 157–193.

    Google Scholar 

  17. Dantzig G., Ramser J. (1959), The truck dispatching problem. Management Science 6, 80–91.

    Google Scholar 

  18. Desaulniers G., Desrosiers J., Erdmann A., Solomon M.M., Soumis F. (2002), VRP with pickup and delivery. In: Toth P., Vigo D. (eds.), The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, 225–242.

    Google Scholar 

  19. Fügenschuh A. (2005), The Integrated Optimization of School Starting Times and Public Bus Services. Logos Verlag, Berlin, ISBN 3-8325-1037-0, 165 pages.

    Google Scholar 

  20. Gaskell T. (1967), Bases for vehicle fleet scheduling. Operation Research Quarterly 18, 367–384.

    Google Scholar 

  21. Ginter V., Kliewer N., Suhl L. (2005), Solving large multi-depot multi-vehicle-type bus scheduling problems in practice. OR Spectrum 27, 507–523.

    Article  Google Scholar 

  22. ILOG CPLEX Division, 889 Alder Avenue, Suite 200, Incline Village, NV 89451, USA. Information available at URL http://www.cplex.com.

  23. Lagarias J.C. (1985), The computational complexity of simultaneous diophantine approximation problems. SIAM Journal on Computing 14, 196–209.

    Article  Google Scholar 

  24. Laporte G., Semet F. (2002), Classical heuristics for the capacitated VRP. In: Toth P., Vigo D. (eds.), The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, 109–128.

    Google Scholar 

  25. Löbel A. (1997), Optimal Vehicle Scheduling in Public Transit. Shaker Verlag, Aachen.

    Google Scholar 

  26. Sherali D., Sivanandan R., Hobeika A.G. (1994), A Linear programming Approach for Synthesizing Origin Destination (O-D) Trip Tables from Link Traffic Volumes. Transportation Research B 28, 213–233.

    Article  Google Scholar 

  27. Stöveken P. (2000), Wirtschaftlicherer Schulverkehr: ÖPNV-Optimierung mit erfolgsabhängiger Honorierung. Der Nahverkehr 3, 65–68. (in German).

    Google Scholar 

  28. Toth P., Vigo D. (2002), The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia.

    Google Scholar 

  29. Wikipedia, the Free Encyclopedia (2004). Online available at URL http://www.wikipedia.org.

  30. Yellow P. (1970), A computational modification to the savings method of vehicle scheduling. Operational Research Quarterly 21, 281–283.

    Article  Google Scholar 

  31. Zabinsky Z.B. (2003), Stochastic Adaptive Search for Global Optimization. Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Boston.

    Google Scholar 

  32. Zabinsky Z.B., Smith R.L., McDonald J.F., Romeijn H.E., Kaufman D.E. (1993), Improving Hit-and-Run for Global Optimization. Journal of Global Optimization 3, 171–192.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Darmstadt University of Technology, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Armin Fügenschuh

Authors
  1. Armin Fügenschuh
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fügenschuh, A. The vehicle routing problem with coupled time windows. cent.eur.j.oper.res. 14, 157–176 (2006). https://doi.org/10.1007/s10100-006-0166-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-006-0166-5

Key words