Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Ahuja RK, Magnanti TL, Orlin JB. Network flows: theory, algorithms and applications. Englewood Cliffs, NJ: Prentice Hall; 1993.
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.
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.
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.
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.
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.
Daganzo CF. The cell transmission model, part II: network traffic. Transport Res B Methodological 1995;29:79–93.
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.
Dantzig GB, Ramser JH. The truck dispatching problem. Manag Sci. 1959;6:80–91.
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.
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.
Fleischmann B, Gietz M, Gnutzmann S. Time-varying travel times in vehicle routing. Transport Sci. 2004;38:160–173.
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.
Haghani A, Jung S. A dynamic vehicle routing problem with time-dependent travel times. Comput Oper Res. 2005;32:2959–2986.
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.
Ichoua S, Gendreau M, Potvin J-Y. Vehicle dispatching with time-dependent travel times. Eur J Oper Res. 2003;144:379–396.
Laporte G. The vehicle routing problem: An overview of exact and approximate algorithms. Eur J Oper Res. 1992;59:345–358.
Larsen A. The dynamic vehicle routing problem. PhD dissertation, Department of Mathematical Modeling, Technical University of Denmark, 2000.
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.
Lysgaard J, Letchford AN, Eglese RW. A new branch-and-cut algorithm for the capacitated vehicle routing problem. Math Program. 2004;100:423–445.
Malandraki C, Daskin MS. Time dependent vehicle routing problems: formulations, properties and heuristic algorithms. Transport Sci. 1992;26:185–200.
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.
Psaraftis HN. Dynamic vehicle routing: status and prospects. Ann Oper Res. 1995;61:143–164.
Schrage L. Formulation and structure of more complex/realistic routing and scheduling problems. Networks 1981;11:229–232.
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.
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.
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.
Toth P, Vigo D (eds.) The vehicle routing problem. SIAM monographs on discrete mathematics and applications. Philadelphia: SIAM; 2002.
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.
Ukkusuri SV, Ramadurai G, Patil G. A robust transportation signal control problem accounting for traffic dynamics. Comput Oper Res. 2010;37:869–879.
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.
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.
Ziliaskopoulos AK. A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transport Sci. 2000;34:37–49.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Aziz, H.M.A., Ukkusuri, S.V. (2013). An Approach to Assess the Impact of Dynamic Congestion in Vehicle Routing Problems. In: Ukkusuri, S., Ozbay, K. (eds) Advances in Dynamic Network Modeling in Complex Transportation Systems. Complex Networks and Dynamic Systems, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6243-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6243-9_11
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6242-2
Online ISBN: 978-1-4614-6243-9
eBook Packages: Business and EconomicsBusiness and Management (R0)