A Hub Location Problem with Fully Interconnected Backbone and Accesss Networks

Tommy Thomadsen, Jesper Larsen

AbstractThis paper considers the design of two-layered fully interconnected networks. A two-layered network consists of clusters of nodes, each defining an access network and a backbone network. We consider the integrated problem of determining the access networks and the backbone network simultaneously. A mathematical formulation is presented, but as the linear programming relaxation of the mathematical formulation is weak, a formulation based on the set partitioning model and column generation approach is also developed.
The column generation subproblems are solved by solving a series of quadratic knapsack problems. We obtain superior bounds using the column generation approach than with the linear programming relaxation. The column generation method is therefore developed into an exact approach using the Branch-and-Price framework. With this approach we are able to solve problems consisting of up to 25 nodes in reasonable time. Given the difficulty of the problem, the results are encouraging.
KeywordsHierarchical networks, Fully interconnected networks, Hub location, Branch-and-Price
TypeJournal paper [With referee]
JournalComputers & Operations Research
Year2007    Month August    Vol. 34    No. 8    pp. 2520-2531
NoteAccepted for publication
BibTeX data [bibtex]
IMM Group(s)Operations Research