Abstract
In this work we address a capacitated hub problem arising from a Telecommunications application. In this problem we must choose the routes and the hubs to use in order to send a set of commodities from sources to destinations in a given capacitated network with a minimum cost. The capacities and costs of the arcs and hubs are given, and the graph connecting the hubs is not assumed to be complete. We present a mixed integer linear programming formulation and describe three different decomposition techniques to get better performances than simply using a direct general solver on the model. These approaches can be applied to deal with more general problems in Network Design.
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
Almiñana, M., Escudero, L.F., Monge, J.F., Sánchez-Soriano, J.: On solving the Enrouting Protocol Problem under uncertainty. In: proceedings of the CORAL meeting, http://webpages.ull.es/users/saderyl/Coral.htm
Barahona, F.: Network Design using cut inequalities. SIAM Journal on Optimization 6, 823–837 (1996)
Benders, J.F.: Partitioning Procedures for Solving Mixed Variables Programming Problems. Numerische Matheamtik 4, 238–252 (1962)
Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72, 387–405 (1994)
Dantzig, G.B., Wolfe, P.: Decomposition Principle for Linar Program. Operations Research 8, 101–111 (1960)
Ebery, J., Krishnamoorthy, M., Ernst, A., Boland, N.: The capacitated multiple allocation hub location problem: Formulations and algorithms. European Journal of Operational Research 120, 614–631 (2000)
Ernst, E., Krishnamoorthy, M.: Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub problem. European Journal of Operational Research 104, 100–112 (1998)
Gabrel, V., Knippel, A., Minoux, M.: Exact solution of multicommodity network optimization problems with general step cost functions. Operations Research Letters 25, 15–23 (1999)
Gondran, M., Minoux, M.: Graphs and algorithms. John Wiley and Sons, Chichester (1984)
Holmberg, K., Yuan, D.: A Langrangian heuristic based branch-and-bound approach for the capacitated network design problem. Operations Research 48, 461–481 (2000)
Magnanti, T.L., Wong, R.T.: Network design and transportation planning: models and algorithms. Transportation Science 18, 1–55 (1984)
Mayer, G., Wagner, B.: HubLocator: an exact solution method for the multiple allocation hub location problem. Computer & Operations Research 29, 715–739 (2002)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley Interscience, Hoboken (1988)
O’Kelly, M., Bryan, D., Skorin-Kapov, D., Skorin-Kapov, J.: Hub network design with single and multiple allocation: A computational study. Location Science 4, 125–138 (1996)
Skorin-Kapov, D., Skorin-Kapov, J., O’Kelly, M.: Tight linear programming relaxations of uncapacitated p-hub median problems. European Journal of Operational Research 94, 582–593 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rodríguez-Martín, I., Salazar-González, JJ. (2004). Decomposition Approaches for a Capacitated Hub Problem. In: Lemaître, C., Reyes, C.A., González, J.A. (eds) Advances in Artificial Intelligence – IBERAMIA 2004. IBERAMIA 2004. Lecture Notes in Computer Science(), vol 3315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30498-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-30498-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23806-5
Online ISBN: 978-3-540-30498-2
eBook Packages: Springer Book Archive