Lagrangean relaxation for the capacitated hub location problem with single assignment

This article considers the capacitated hub location problem with single assignment. We propose a Lagrangean relaxation to obtain tight upper and lower bounds. The Lagrangean function that we formulate exploits the structure of the problem and can be decomposed into smaller subproblems that can be solved efficiently. In addition, we present some simple reduction tests, based on the Lagrangean relaxation bounds that allows us to reduce considerably the size of the formulation and thus, to reduce the computational effort. Computational experiments have been performed with both benchmark instances from literature and with some new larger instances. The obtained results are impressive. For all tested instances (ranging from 10 to 200 nodes), we obtain or improve the best known solution and the obtained duality gaps, between our upper and lower bounds, never exceed 3.4%.