Abstract
In this chapter we discuss the Vehicle Routing Problem with Time Windows in terms of its mathematical modeling, its structure and decomposition alternatives. We then present the master problem and the subproblem for the column generation approach, respectively. Next, we illustrate a branch-and-bound framework and address acceleration strategies used to increase the efficiency of branch-and-price methods. Then, we describe generalizations of the problem and report computational results for the classic Solomon test sets. Finally, we present our conclusions and discuss some open problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ascheuer, N., Fischetti, M., and Grötschel, M. (2000). Polyhedral study of the asymmetric traveling salesman problem with time windows. Networks 36:69–79.
Ascheuer, N., Fischetti, M., and Grötschel, M. (2001). Solving the asymmetric travelling salesman problem with time windows by branch-and-cut. Mathematical Programming 90:475–506.
Balas, E., Fischetti, M., and Pulleyblank, W.R. (1995). The precedence-constrained asymmetric travelling salesman polytope. Mathematical Programming 68:241–265.
Bard, J., Kontoravdis, G., and Yu, G. (2002). A Branch-and-cut procedure for the vehicle routing problem with time windows. Transportation Science 36:250–269.
Chabrier, A. (2005). Vehicle routing problem with elementary shortest path based column generation. Forthcoming in: Computers and Operations Research.
Chabrier, A., Danna, E., and Claude Le Pape. (2002). Coopération entre génération de colonnes avec tournées sans cycle et recherche locale appliquée au routage de véhicules. In: Huitièmes Journées Nationales sur la Résolution de Problèmes NP-Complets (JNPC 2002).
Cook, W. and Rich, J.L. (1999). A parallel cutting-plane algorithm for the vehicle routing problem with time windows. Technical report TR99-04. Department of Computational and Applied Mathematics, Rice University.
Cordeau, J.-F., Desaulniers, G., Desrosiers, J., and Soumis, F. (2002). The VRP with time windows. In: The vehicle routing problem (P. Toth and D. Vigo, eds.), pp. 157–193, SIAM Monographs on Discrete Mathematics and its Applications.
Crowder, H. and Padberg, M. (1980). Solving large-scale symmetric travelling salesman problems to optimality. Management Science 26:495–509.
Danna, E. and Le Pape, C. (2005). Accelerating branch-and-price with local search: A case study on the vehicle routing problem with time windows. This volume.
Desaulniers, G., Desrosiers, J., and Solomon, M.M. (2002). Accelerating Strategies in column generation methods for vehicle routing and crew scheduling problems. In: Essays and Surveys in Metaheuristics (C. Ribeiro and P. Hansen, eds.), pp. 309–324, Kluwer Academic Publishers.
Desrosiers, M., Desrosiers, J., and Solomon, M.M. (1992). A new optimization algorithm for the vehicle routing problem with time windows. Operations Research 40:342–354.
Desrochers, M. and Soumis, F. (1988). A generalized permanent labelling algorithm for the shortest path problem with time windows. INFORMS 26:191–212.
Desrosiers, J., Dumas, Y., Solomon, M. M., and Soumis, F. (1995). Time constrained routing and scheduling. In: Handbooks in Operations Research and Management Sciences (M. Ball, T. Magnanti, C. Monma and G. Nemhauser, eds.), vol. 8, Network Routing, pp. 35–139, North-Holland, Amsterdam.
Desrosiers, J., Sauvé, M., and Soumis, F. (1988). Lagrangean relaxation methods for solving the minimum fleet size multiple travelling-salesman problem with time windows. Management Science 34:1005–1022.
Dror, M. (1994). Note on the complexity of the shortest path models for column generation in VRPTW. Operations Research 42:977–978.
Dumitrescu, I., and Boland, N. (2003). Improved preprocessing, labeling and scaling algorithms for the weight-constrained shortest path problem. Networks 42:135–153.
Feillet, D., Dejax, P., Gendreau, M., and Gueguen, C. (2004). An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks 44:216–229.
Gélinas, S., Desrochers, M., Desrosiers, J., and Solomon, M.M. (1995). A new branching strategy for time constrained routing problems with application to backhauling. Annals of Operations Research 61:91–109.
Halse, K. (1992). Modeling and solving complex vehicle routing problems. Ph.D Thesis, Technical University of Denmark.
Homberger, J. and Gehring, H. (1999). Two evolutionary metaheuristics for the vehicle routing problem with time windows. INFORMS 37:297–318.
Ioachim, I., Gélinas, S., Desrosiers, J., and Soumis F. (1998). A dynamic programming algorithm for the shortest path problem with time windows and linear node costs. Networks, 31:193–204.
Irnich, S. and Villerieuve, D. (2005). The shortest path problem with κ-cycle elimination (κ ≥ 3): Improving a branch-and-price algorithm for the VRPTW. Forthcoming in: INFORMS Journal of Computing.
Jörnsten, K., Madsen, O.B.G., and Sørensen, B. (1986). Exact solution of the vehicle routing and scheduling problem with time windows by variable splitting, Research Report 5/1986, Institute of Mathematical Statistics and Operations Research, Technical University of Denmark.
Kallehauge, B. (2000). Lagrangian duality and non-differentiable optimization—Applied on vehicle routing [in Danish]. Master’s Thesis, Technical University of Denmark.
Kallehauge, B. and Boland, N. (2004). Infeasible path inequalities for the vehicle routing problem with time windows. Technical Report, Centre for Traffic and Transport, Technical University of Denmark.
Kallehauge, B., Larsen, J., and Madsen, O.B.G. (2000). Lagrangean duality and non-differentiable optimization applied on routing with time windows—Experimental results. Technical Report IMM-REP-2000-8, Department of Mathematical Modelling, Technical University of Denmark.
Kohl, N. (1995). Exact methods for time constrained routing and related scheduling problems. Ph.D Thesis, Technical University of Denmark.
Kohl, N., Desrosiers, J., Madsen, O.B.G., Solomon, M.M., and Soumis, F. (1999). 2-path cuts for the vehicle routing problem with time windows. Transportation Science 33:101–116.
Kohl, N. and Madsen, O.B.G. (1997). An optimization algorithm for the vehicle routing problem with time windows based on Lagrangean relaxation. Operations Research 45:395–403.
Kolen, A.W.J., Rinnooy Kan, A.H.G., and Trienekens, H.W.J.M. (1987). Vehicle routing with time windows. Operations Research 35:266–273.
Kontoravdis, G. and Bard, J.F. (1995). A GRASP for the vehicle routing problem with time windows. ORSA Journal on Computing 7:10–23.
Laporte, G., Nobert, Y., and Desrochers, M. (1985). Optimal routing under capacity and distance restrictions. Operations Research 33:1050–1073.
Larsen, J. (1999). Parallelization of the vehicle routing problem with time windows. Ph.D Thesis, Technical University of Denmark.
Larsen, J. (2004). Refinements of the column generation process for the vehicle routing problem with time windows. Journal of Systems Science and Systems Engineering 13(3):326–341.
Mak, V.H. (2001). On the asymmetric travelling salesman problem with replenishment arcs. Ph.D Thesis, Department of Mathematics and Statistics, The University of Melbourne.
du Merle, O., Villeneuve, D., Desrosiers, J., and Hansen, P. (1999). Stabilized column generation. Discrete Mathematics 199:229–237.
Naddef, D., and Rinaldi, G. (2002). Branch-and-cut algorithms for the capacitated VRP. In: The Vehicle Routing Problem (P. Toth and D. Vigo, eds.), SIAM Monographs on Discrete Mathematics and Applications, pp. 53–84, SIAM, Philadelphia.
Rousseau, L.-M., Gendreau, M., and Pesant, G. (2004). Solving VRPTWs with constraint programming based column generation. Annals of Operations Research 130:199–216.
Solomon, M.M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35:254–265.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Kallehauge, B., Larsen, J., Madsen, O.B., Solomon, M.M. (2005). Vehicle Routing Problem with Time Windows. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds) Column Generation. Springer, Boston, MA. https://doi.org/10.1007/0-387-25486-2_3
Download citation
DOI: https://doi.org/10.1007/0-387-25486-2_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25485-2
Online ISBN: 978-0-387-25486-9
eBook Packages: Business and EconomicsBusiness and Management (R0)