Abstract
The multiple allocation uncapacitated hub location problem is considered. This problem arises in transportation systems when several locations send and receive passengers and/or express packages and the performance of these systems can be improved by using transshipment points (hubs), where the passengers/packages are collected and distributed.
An Integer Programming formulation, the one giving the best computational results until now, serves as a basis for the solution method. Using the fact that the transportation costs between hubs satisfy the triangle inequality, an analysis of the set of solutions that are not candidates to be optimal is carried out and, as a consequence, the formulation of the problem can be strengthened by means of powerful valid inequalities obtained through the study of the intersection graph of an associated set packing problem. The algorithm developed uses the most promising of these inequalities in a Lagrangian relaxation context to reduce the size of the branching tree and improve the computational times. This improvement is shown by means of a computational study, where a set of instances are optimally solved with low computational effort.
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References
P. Avella A. Sassano (2001) ArticleTitleOn the p-median polytope Mathematical Programming 89 395–411
Boland, N., Krishnamoorthy, M., Ernst, A.T. and Ebery, J. (in press), Preprocessing and cutting for multiple allocation hub location problems, European Journal of Operational Research.
J.F. Campbell (1994) ArticleTitleInteger programming formulations of discrete hub location problems European Journal of Operational Research 72 387–405 Occurrence Handle10.1016/0377-2217(94)90318-2
Cánovas, L., Landete, M. and Marín, A. (2001), Improved formulations for the uncapacitated multiple allocation hub location problem, Working Paper submitted for publication, Departamento de Estad´ıstica e Investigaci ´on Operativa, University of Murcia, Spain.
D.C. Cho E.L. Johnson M.W. Padberg M.R. Rao (1983) ArticleTitleOn the Uncapacitated Plant Location Problem I: valid inequalities and facets Mathematics of Operations Research 8-4 579–589
A. Ernst M. Krishnamoorthy (1998a) ArticleTitleAn exact solution approach based on shortest-paths for p-hub median problems INFORMS Journal on Computing 10 149–162 Occurrence Handle10.1287/ijoc.10.2.149
A. Ernst M. Krishnamoorthy (1998b) ArticleTitleExact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem European Journal of Operational Research 104 100–112
M. Guignard (1998) ArticleTitleEfficient cuts in Lagrangean ‘Relax-and-cut’ schemes European Journal of Operational Research 105 216–223 Occurrence Handle10.1016/S0377-2217(97)00034-9
H.W. Hamacher M. Labbé S. Nickel T. Sonneborn (2001) Polyhedral properties of the uncapacitated multiple allocation hub location problem ITWM Kaiserslautern, Germany
J.G. Klincewicz (1996) ArticleTitleA dual algorithm for the uncapacitated hub location problem Location Science 4 173–184 Occurrence Handle10.1016/S0966-8349(96)00010-1
G. Mayer B. Wagner (2002) ArticleTitleHubLocator: an exact solution method for the multiple allocation hub location problem Computers and Operations Research 29 715–739 Occurrence Handle10.1016/S0305-0548(01)00080-6
G.L. Nemhauser L.E. Trotter SuffixJr. (1974) ArticleTitleProperties of vertex packing and independence system polyhedra Mathematical Programming 6 48–61 Occurrence Handle10.1007/BF01580222
M.E. O’Kelly D. Bryan D. Skorin-Kapov J. Skorin-Kapov (1996) ArticleTitleHub network design with single and multiple allocation: A computational study Location Science 4 125–138
M.W. Padberg (1973) ArticleTitleOn the facial structure of set packing polyhedra Mathematical Programming 5 199–215 Occurrence Handle10.1007/BF01580121
M.W. Padberg (1977) ArticleTitleOn the complexity of set packing polyhedra Annals of Discrete Mathematics 1 421–434
D. Skorin-Kapov J. Skorin-Kapov M. O’Kelly (1996) ArticleTitleTight linear programming relaxations of uncapacitated p-hub median problems European Journal of Operational Research 94 582–593 Occurrence Handle10.1016/0377-2217(95)00100-X
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Marín, A. Uncapacitated Euclidean Hub Location: Strengthened Formulation, New Facets and a Relax-and-cut Algorithm. J Glob Optim 33, 393–422 (2005). https://doi.org/10.1007/s10898-004-6099-4
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DOI: https://doi.org/10.1007/s10898-004-6099-4