Summary
This chapter presents techniques for constructing robust Branch-Cut-and-Price algorithms on a number of Vehicle Routing Problem variants. The word ‘‘robust’’ stresses the effort of controlling the worst-case complexity of the pricing subproblem, keeping it pseudo-polynomial. Besides summarizing older research on the topic, some promising new lines of investigation are also presented, specially the development of new families of cuts over large extended formulations. Computational experiments over benchmark instances from ACVRP, COVRP, CVRP and HFVRP variants are provided.
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
N. Achuthan, L. Caccetta, and S. Hill. Capacited vehicle routing problem: Some new cutting planes.Asia-Pacific J. of Operational Research, 15:109–123, 1998.
J. Araque, L. Hall, and T. Magnanti. Capacitated trees, capacitated routing, and associated polyhedra. Technical Report OR232-90, MIT, Operations Research Center, 1990.
P. Augerat.Approche poly‘edrale du probl‘eme de tourn’ees de v’ehicles. PhD thesis, Institut National Polytechnique de Grenoble, 1995.
P. Augerat, J. Belenguer, E. Benavent, A. Corber’an, D. Naddef, and G. Rinaldi. Computational results with a branch and cut code for the capacitated vehicle routing problem. Technical Report 949-M, Université Joseph Fourier, Grenoble, France, 1995.
R. Baldacci, L. Bodin, and A. Mingozzi. The multiple disposal facilities and multiple inventory locations rollon-rolloff vehicle routing problem.Computers and Operation Research, 33:2667–2702, 2006.
R. Baldacci, N. Christofides, and A. Mingozzi. An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Submitted, 2007.
C. Barnhart, C. Hane, and P. Vance. Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems.Operations Research, 40:318–326, 2000.
C. Barnhart, E. Johnson, G. Nemhauser, M. Savelsbergh, and P. Vance. Branch-and-price: Column generation for solving huge integer programs.Operations Research, 46:316–329, 1998.
E. Choi and D-W Tcha. A column generation approach to the heterogeneous fleet vehicle routing problem.Computers and Operations Research, 34:2080–2095, 2007.
N. Christofides and S. Eilon. An algorithm for the vehicle-dispatching problem.Operational Research Quarterly, 20:309–318, 1969.
N. Christofides, A. Mingozzi, and P. Toth. Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations.Mathematical Programming, 20:255–282, 1981.
G. Cornu’ejols and F. Harche. Polyhedral study of the capacitated vehicle routing problem.Mathematical Programming, 60:21–52, 1993.
S. Dash, R. Fukasawa, and O. Gunluk. On the generalized master knapsack polyhedron. InProceedings of the IPCO 2007, 2007.
du Merle, O. Villeneuve, J. Desrosiers, and P. Hansen. Stabilized column generation.Discrete Mathematics, 194:229–237, 1999.
G. Felici, C. Gentile, and G. Rinaldi. Solving large MIP models in supply chain management by branch & cut. Technical report, Istituto di Analisi dei Sistemi ed Informatica del CNR, Italy, 2000.
M. Fischetti, P. Toth, and D. Vigo. A branch and bound algorithm for the capacitated vehicle routing problem on directed graphs.Operations Research, 42:846–859, 1994.
R. Fukasawa, H. Longo, J. Lysgaard, M. Poggi de Aragão, M. Reis, E. Uchoa, and R. F. Werneck. Robust branch-and-cut-and-price for the capacitated vehicle routing problem.Mathematical Programming, 106:491–511, 2006.
R. Fukasawa, M. Reis, M. Poggi de Aragão, and E. Uchoa. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Technical Report RPEP Vol.3 no.8, Universidade Federal Fluminense, Engenharia de Produção, Niter’oi, Brazil, 2003.
M. T. Godinho, L. Gouveia, and T. Magnanti. Combined route capacity and path length models for unit demand vehicle routing problems.InProceedings of the INOC, volume 1, pages 8–15, Lisbon, 2005.
B. Golden, A. Assad, L. Levy, and F. Gheysens. The fleet size and mix vehicle routing problem.Computers and Operations Research, 11:49–66, 1984.
L. Hall and T. Magnanti. A polyhedral intersection theorem for capacitated spanning trees.Mathematics of Operations Research, 17, 1992.
D. Houck, J. Picard, M. Queyranne, and R. Vegamundi. The travelling salesman problem as a constrained shortest path problem.Opsearch, 17:93–109, 1980.
S. Irnich and D. Villeneuve. The shortest path problem with resource constraints and k-cycle elimination for k⩾ 3.INFORMS Journal on Computing, 18:391–406, 2006.
M. Jepsen, S. Spoorendonk, B. Petersen, and D. Pisinger. A non-robust branch-and-cut-and-price for the vehicle routing problem with time windows. Technical Report 06/03, University of Copenhagen, 2006.
B. Kallehauge, N. Boland, and O. Madsen. Path inequalities for the vehicle routing problem with time windows. Technical report, Technical University of Denmark, 2005.
D. Kim, C. Barnhart, K. Ware, and G. Reinhardt. Multimodal express package delivery: A service network design application.Transportation Science, 33:391–407, 1999.
N. Kohl, J. Desrosiers, O. Madsen, M. Solomon, and F. Soumis. 2-Path cuts for the vehicle routing problem with time windows.Transportation Science, 33:101–116, 1999.
A. Letchford, R. Eglese, and J. Lysgaard. Multistars, partial multistars and the capacitated vehicle routing problem.Mathematical Programming, 94:21–40, 2002.
A. Letchford, J. Lysgaard, and R. Eglese. A branch-and-cut algorithm for the capacitated open vehicle routing problem.Journal of the Operational Research Society, 2007.
A. Letchford and J-J. Salazar. Projection results for vehicle routing.Mathematical Programming, 105:251–274, 2006.
J. Lysgaard. Reachability cuts for the vehicle routing problem with time windows.European Journal of Operational Research, 175:210–233, 2006.
J. Lysgaard, A. Letchford, and R. Eglese. A new branch-and-cut algorithm for the capacitated vehicle routing problem.Mathematical Programming, 100:423–445, 2004.
D. Naddef and G. Rinaldi. Branch-and-cut algorithms for the capacitated VRP. In P. Toth and D. Vigo, editors,The Vehicle Routing Problem, chapter 3, pages 53–84. SIAM, 2002.
J. Picard and M. Queyranne. The time-dependant traveling salesman problem and its application to the tardiness problem in one-machine scheduling.Operations Research, 26:86–110, 1978.
M. Poggi de Aragão and E. Uchoa. Integer program reformulation for robust branch-and-cut-and-price. In L. Wolsey, editor,Annals of Mathematical Programming in Rio, pages 56–61, Bùzios, Brazil, 2003.
E. Uchoa, R. Fukasawa, J. Lysgaard, A. Pessoa, M. Poggi de Aragão, and D. Andrade. Robust branch-and-cut-and-price for the capacitated vehicle routing problem.Mathematical Programming, on-line first, 2007.
J. Van den Akker, C. Hurkens, and M. Savelsbergh. Time-indexed formulation for machine scheduling problems: column generation.INFORMS J. on Computing, 12:111–124, 2000.
F. Vanderbeck. Lot-sizing with start-up times.Management Science, 44:1409–1425, 1998.
H. Yaman. Formulations and valid inequalities for the heterogeneous vehicle routing problem.Mathematical Programming, 106:365–390, 2006.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Pessoa, A., de Aragão, M., Uchoa, E. (2008). Robust Branch-Cut-and-Price Algorithms for Vehicle Routing Problems. In: Golden, B., Raghavan, S., Wasil, E. (eds) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77778-8_14
Download citation
DOI: https://doi.org/10.1007/978-0-387-77778-8_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-77777-1
Online ISBN: 978-0-387-77778-8
eBook Packages: Business and EconomicsBusiness and Management (R0)