Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation algorithms for the optimal p-source communication spanning tree
Discrete Applied Mathematics
Locating tree-shaped facilities using the ordered median objective
Mathematical Programming: Series A and B
Formulating and solving splittable capacitated multiple allocation hub location problems
Computers and Operations Research - Articles presented at the conference on routing and location (CORAL)
Hub Arc Location Problems: Part I-Introduction and Results
Management Science
Hub Arc Location Problems: Part II-Formulations and Optimal Algorithms
Management Science
Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment
INFORMS Journal on Computing
Star p-hub center problem and star p-hub median problem with bounded path lengths
Computers and Operations Research
Computers and Industrial Engineering
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This paper considers the tree of hub location problem. We propose a four index formulation which yields much tighter LP bounds than previously proposed formulations, although at a considerable increase of the computational burden when obtained with a commercial solver. For this reason we propose a Lagrangean relaxation, based on the four index formulation, that exploits the structure of the problem by decomposing it into independent subproblems which can be solved quite efficiently. We also obtain upper bounds by means of a simple heuristic that is applied at the inner iterations of the method that solves the Lagrangean dual. As a consequence, the proposed Lagrangean relaxation produces tight upper and lower bounds and enable us to address instances up to 100 nodes, which are notably larger than the ones previously considered in the literature, with sizes up to 20 nodes. Computational experiments have been performed with benchmark instances from the literature. The obtained results are remarkable. For most of the tested instances we obtain or improve the best known solution and for all tested instances the deviation between our upper and lower bounds, never exceeds 10%.