Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment

This paper presents a branch-and-price algorithm for the capacitated hub location problem with single assignment, in which Lagrangean relaxation is used to obtain tight lower bounds of the restricted master problem. A lower bound that is valid at any stage of the column generation algorithm is propo...

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Bibliographic Details
Published inINFORMS journal on computing Vol. 23; no. 1; pp. 41 - 55
Main Authors Contreras, Ivan, Diaz, Juan A, Fernandez, Elena
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.01.2011
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Branch & bound algorithms
column generation
hub location
Lagrange multiplier
Lagrangean relaxation
Network hubs
Optimization algorithms
Relaxation methods (Mathematics)
Studies
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Summary:This paper presents a branch-and-price algorithm for the capacitated hub location problem with single assignment, in which Lagrangean relaxation is used to obtain tight lower bounds of the restricted master problem. A lower bound that is valid at any stage of the column generation algorithm is proposed. The process to obtain this valid lower bound is combined with a constrained stabilization method that results in a considerable improvement on the overall efficiency of the solution algorithm. Numerical results on a battery of benchmark instances of up to 200 nodes are reported. These seem to be the largest instances that have been solved to optimality for this problem.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1100.0391