An Approach to Assess the Impact of Dynamic Congestion in Vehicle Routing Problems

  • H. M. Abdul Aziz
  • Satish V. UkkusuriEmail author
Part of the Complex Networks and Dynamic Systems book series (CNDS, volume 2)


This research proposes an integrated framework of capacitated vehicle routing problems (CVRP) and traffic flow model (cell transmission model in this research) to assess the effect of time-varying congestion. We develop a framework consisting sequence of mixed integer programs solving the CVRP with updated cost obtained from the traffic flow model. A real-world network with 15 cities and towns is tested with the framework and results show significant travel time reduction from the case where time-varying congestion is not considered. In addition, we consider system optimal type of route choice behavior within the traffic flow model.


Travel Time Vehicle Rout Problem Cost Matrix Total Travel Time Traffic Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Ahuja RK, Magnanti TL, Orlin JB. Network flows: theory, algorithms and applications. Englewood Cliffs, NJ: Prentice Hall; 1993.Google Scholar
  2. Augerat P, Belenguer JM, Benavent E, Corberan A, Naddef D, Rinaldi G. Computational results with a branch and cut code for the capacitated vehicle routing problem. In: Grenoble editor. France: Institut d’informatique et de mathématiques appliquées de Grenoble; 1995. p. 30.Google Scholar
  3. Chang M-S, Hsueh C-F, Chen S-R. Real-time vehicle routing problem with time windows and simultaneous delivery/pickup demands. J Eastern Asia Soc Transport Stud. 2003;5:2273–2286.Google Scholar
  4. Chen H-K, Hsueh C-F, Chang M-S. The real-time time-dependent vehicle routing problem. Transport Res E Logist Transport Rev. 2006;42:383–408.CrossRefGoogle Scholar
  5. Conrad R, Figliozzi M. Algorithms to quantify impact of congestion on time-dependent real-world urban freight distribution networks. Transport Res Rec J Transport Res Board 2168, Washington, D.C.: Transportation Research Board of the National Academies; 2010, p. 104–113.Google Scholar
  6. Cordeau JF, Laporte G, Mercier A. A unified tabu search heuristic for vehicle routing problems with time windows. J Oper Res Soc. 2001;52:928–936.CrossRefGoogle Scholar
  7. Daganzo CF. The cell transmission model, part II: network traffic. Transport Res B Methodological 1995;29:79–93.CrossRefGoogle Scholar
  8. Daganzo CF. The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transport Res B Methodological 1994;28:269–287.CrossRefGoogle Scholar
  9. Dantzig GB, Ramser JH. The truck dispatching problem. Manag Sci. 1959;6:80–91.CrossRefGoogle Scholar
  10. Donati AV, Montemanni R, Casagrande N, Rizzoli AE, Gambardella LM. Time dependent vehicle routing problem with a multi ant colony system. Eur J Oper Res. 2008;185:1174–1191.CrossRefGoogle Scholar
  11. Figliozzi MA. Analysis of the efficiency of urban commercial vehicle tours: Data collection, methodology, and policy implications. Transport Res B Methodological 2007;41:1014–1032.CrossRefGoogle Scholar
  12. Fleischmann B, Gietz M, Gnutzmann S. Time-varying travel times in vehicle routing. Transport Sci. 2004;38:160–173.CrossRefGoogle Scholar
  13. Fukasawa R, Longo H, Lysgaard J, Aragão MP, d Reis M, Uchoa E, Werneck RF. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math Program. 2006;106:491–511.Google Scholar
  14. Haghani A, Jung S. A dynamic vehicle routing problem with time-dependent travel times. Comput Oper Res. 2005;32:2959–2986.CrossRefGoogle Scholar
  15. Hu T-Y, Liao T-Y, Lu Y-C. Study of solution approach for dynamic vehicle routing problems with real-time information. Transport Res Rec J Transport Res Board 1857, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 102–108.Google Scholar
  16. Ichoua S, Gendreau M, Potvin J-Y. Vehicle dispatching with time-dependent travel times. Eur J Oper Res. 2003;144:379–396.CrossRefGoogle Scholar
  17. Laporte G. The vehicle routing problem: An overview of exact and approximate algorithms. Eur J Oper Res. 1992;59:345–358.CrossRefGoogle Scholar
  18. Larsen A. The dynamic vehicle routing problem. PhD dissertation, Department of Mathematical Modeling, Technical University of Denmark, 2000.Google Scholar
  19. Lighthill MJ, Whitham GB. On kinematic waves II: A theory of traffic flow on long crowded roads. In Proceedings of the royal society of london series a-mathematical and physical sciences, 1955, p. 317–345.Google Scholar
  20. Lysgaard J, Letchford AN, Eglese RW. A new branch-and-cut algorithm for the capacitated vehicle routing problem. Math Program. 2004;100:423–445.CrossRefGoogle Scholar
  21. Malandraki C, Daskin MS. Time dependent vehicle routing problems: formulations, properties and heuristic algorithms. Transport Sci. 1992;26:185–200.CrossRefGoogle Scholar
  22. Malandraki C, Dial RB. A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem. Eur J Oper Res. 1996;90:45–55.CrossRefGoogle Scholar
  23. Psaraftis HN. Dynamic vehicle routing: status and prospects. Ann Oper Res. 1995;61:143–164.CrossRefGoogle Scholar
  24. Schrage L. Formulation and structure of more complex/realistic routing and scheduling problems. Networks 1981;11:229–232.CrossRefGoogle Scholar
  25. Shieh H-M, May M-D. On-line vehicle routing with time windows: optimization-based heuristics approach for freight demands requested in real-time. Transport Res Rec J Transport Res Board 1617, Washington, D.C.: Transportation Research Board of the National Academies; 1998, p. 171–178.Google Scholar
  26. Stickel M, Darger J, Furmans K. Vehicle routing with regard to traffic prognosis and congestion probabilities. Adv OR AI Method Transport. 2005;1:780–786.Google Scholar
  27. Taniguchi E, Thompson R. Modeling city logistics. Transport Res Rec J Transport Res Board 1790, Washington, D.C.: Transportation Research Board of the National Academies; 2002. p. 45–51.Google Scholar
  28. Toth P, Vigo D (eds.) The vehicle routing problem. SIAM monographs on discrete mathematics and applications. Philadelphia: SIAM; 2002.Google Scholar
  29. Ukkusuri SV, Waller ST. Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions. Network Spatial Econ. 2008;8:383–406.CrossRefGoogle Scholar
  30. Ukkusuri SV, Ramadurai G, Patil G. A robust transportation signal control problem accounting for traffic dynamics. Comput Oper Res. 2010;37:869–879.CrossRefGoogle Scholar
  31. Woensel TV, Kerbache L, Peremans H, Vandaele N. Vehicle routing with dynamic travel times: A queueing approach. Eur J Oper Res. 2008;186:990–1007.CrossRefGoogle Scholar
  32. Zheng H, Chiu Y-C. A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem. Transport Sci. 2011;45:121–137.CrossRefGoogle Scholar
  33. Ziliaskopoulos AK. A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transport Sci. 2000;34:37–49.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Civil EngineeringPurdue UniversityWest LafayetteUSA

Personalised recommendations