Summary
Capacitated vehicle routing problems (CVRPs) form the core of logistics planning and are hence of great practical and theoretical interest. This chapter considers the CVRP on trees (TCVRP), a problem that often naturally arises in railway, river, and rural road networks. Our objective is to build high-quality models that exploit the tree structure of the problem that can also be easily implemented within the framework of a modeling language (a feature desired by practitioners) like AMPL, GAMS, or OPL. We present two new integer programming models for the TCVRP that explicitly take advantage of the tree structure of the graph. The two models are implemented using the AMPL model building language, and compared along several metrics—computation time, quality of the linear programming relaxation, and scalability—to examine their relative strengths.
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References
C. Basnet, L.R. Foulds, and J.M. Wilson. Heuristics for vehicle routing on tree-like networks.Journal of the Operational Research Society, 50:627–635, 1999.
I. Berger, J.-M. Bourjolly, and G. Laporte. Branch-and-bound algorithms for the multi-product assembly line balancing problem.European Journal of Operational Research, 58:215–222, 1992.
G. Clarke and J. Wright. Scheduling of vehicles from a central depot to a number of delivery points.Operations Research, 12:568–581, 1964.
E. G. Coffman, M. R. Garey, and D. S. Johnson. Approximation algorithms for bin packing – an updated survey. In G. Ausiello, M. Lucertini, and P. Serafini, editors,Algorithms design for computer system design, pages 49–106. Springer-Verlag, New York, 1984.
R. Fourer, D. M. Gay, and B. W. Kernighan.AMPL: A Modeling Language for Mathematical Programming. The Scientific Press, 1993.
ILOG. Cplex 9.0 reference manual, 2003.
J. Kallrath, editor.Modeling Languages in Mathematical Optimization, volume 88 ofApplied Optimization. Springer Publishing Company, 2004.
M. Labb´e, G. Laporte, and H. Mercure. Capacitated vehicle routing on trees.Operations Research, 39:616–622, 1991.
P. Mbaraga, A. Langevin, and G. Laporte. Two exact algorithms for the vehicle routing problem on trees.Naval Research Logistics, 46:75–89, 1999.
G. L. Nemhauser and L. A. Wolsey.Integer and Combinatorial Optimization. John Wiley and Sons, New York, 1988.
P. Toth and D. Vigo, editors.The Vehicle Routing Problem, volume 9 of SIAM Monographs on Discrete Mathematics and Applications.SIAM, Philadelphia, PA, 2002.
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Chandran, B., Raghavan, S. (2008). Modeling and Solving the Capacitated Vehicle Routing Problem on Trees. 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_11
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DOI: https://doi.org/10.1007/978-0-387-77778-8_11
Publisher Name: Springer, Boston, MA
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