Summary
Inter-tour constraints are constraints in a vehicle-routing problem (VRP) on globally limited resources that different vehicles compete for.% Real-world examples are a limited number of ‘‘long’’ tours, where long is defined with respect to the traveled distance, the number of stops, the arrival time at the depot etc. % Moreover, a restricted number of docking stations or limited processing capacities for incoming goods at the destination depot can be modeled by means of inter-tour resource constraints.% In this chapter, we introduce a generic model for VRPs with inter-tour constraints based on the giant-tour representation and resource-constrained paths.% Furthermore, solving the model by efficient local search techniques is addressed: % Tailored preprocessing procedures and feasibility tests are combined into local-search algorithms, that are attractive from a worst-case point of view and are superior to traditional search techniques in the average case. % In the end, the chapter provides results for some new types of studies where VRPs with time-varying processing capacities are analyzed.
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
E. Aarts and J. Korst.Simulated Annealing and Boltzmann Machines. Wiley, Chichester, 1989.
P. Avella, M. Boccia, and A. Sforza. Resource constrained shortest path problems in path planning for fleet management.Journal of Mathematical Modelling and Algorithms, 3:1–17, 2004.
O. Bräysy and M. Gendreau. Vehicle routing with time windows, Part I: Route construction and local search algorithms.Transportation Science, 39:104–118, 2005.
O. Bräysy and M. Gendreau. Vehicle routing with time windows, Part II: Metaheuristics.Transportation Science, 39:119–139, 2005.
N. Christofides and S. Eilon. An algorithm for the vehicle-dispatching problem.Operational Research Quarterly, 20:309–318, 1969.
N. Christofides and S. Eilon. Algorithms for large-scale travelling salesman problems.Operational Research Quarterly, 23:511–518, 1972.
G. Desaulniers, J. Desrosiers, I. Ioachim, M.M. Solomon, F. Soumis, and D. Villeneuve. A unified framework for deterministic time constrained vehicle routing and crew scheduling problems, Chapter 3 inFleet Management and Logistics, T. Crainic and G. Laporte, eds., Kluwer Academic Publisher, Boston, 1998.
B. Funke, T. Grünert, and S. Irnich. Local search for vehicle routing and scheduling problems: Review and conceptual integration.Journal of Heuristics, 11:267–306, 2005.
P. Hansen and N. Mladenovi´c. Variable neighborhood search: Principles and applications.European Journal of Operational Research, 130:449–467, 2001.
S. Irnich. Resource extension functions: Properties, inversion, and generalization to segments. Technical Report 2006-01, Deutsche Post Endowed Chair of Optimization of Distribution Networks, RWTH Aachen University, Aachen, Germany, 2006. Available at www.dpor.rwth-aachen.de, forthcoming in OR Spectrum.
S. Irnich. A unified modeling and solution framework for vehicle routing and local search-based metaheuristics. Technical Report 2006-02, Deutsche Post Endowed Chair of Optimization of Distribution Networks, RWTH Aachen University, Aachen, Germany, 2006. Available at www.dpor.rwth-aachen.de, accepted with minor modifications for publication in INFORMS Journal on Computing.
S. Irnich and G. Desaulniers. Shortest path problems with resource constraints, Chapter 2 inColumn Generation, G. Desaulniers, J. Desrosiers, and M.M. Solomon, eds., Springer, 2005.
S. Irnich, B. Funke, and T. Grünert. Sequential search and its application to vehicle-routing problems.Computers & Operations Research, 33:2405–2429, 2006.
B.W. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs.Bell Syst. Tech. J., 49:291–307, 1970.
G.A.P. Kindervater and M.W.P. Savelsbergh. Vehicle routing: Handling edge exchanges, Chapter 10 inLocal Search in Combinatorial Optimization, E. Aarts and J. Lenstra, eds., Wiley, Chichester, 1997.
S. Lin and B.W. Kernighan. An effective heuristic algorithm for the traveling-salesman problem.Operations Research, 21:498–516, 1973.
O. Martin, S.W. Otto, and E.W. Felten. Large-step Markov chains for the TSP incorporating local search heuristics.Operations Research Letters, 11:219–224, 1992.
N. Mladenovi´c and P. Hansen. Variable neighborhood search.Computers & Operations Research, 24:1097–1100, 1997.
D. Pisinger and S. Røpke. A general heuristic for vehicle routing problems.Computers & Operations Research, 34:2403–2435, 2007.
J.-Y. Potvin, G. Lapalme, and J.-M. Rousseau. A generalized k-opt exchange procedure for the MTSP.Information Systems and Operations Research, 27:474–481, 1989.
S. Røpke and D. Pisinger. An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows.Transportation Science, 40:455–472, 2006.
M.W.P. Savelsbergh. Local search for routing problems with time windows. inAlgorithms and Software for Optimization, Part I, C.L. Monma, ed., Baltzer, Basel, Volume 4:285–305, 1986.
M.W.P. Savelsbergh. An efficient implementation of local search algorithms for constrained routing problems.European Journal of Operational Research, 47:75–85, 1990.
P. Shaw. Using constraint programming and local search methods to solve vehicle routing problems.Lecture Notes in Computer Science, Volume 1520:417–431, 1998.
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
Hempsch, C., Irnich, S. (2008). Vehicle Routing Problems with Inter-Tour Resource Constraints. 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_19
Download citation
DOI: https://doi.org/10.1007/978-0-387-77778-8_19
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)