The Dynamic Uncapacitated Hub Location Problem

This paper presents a dynamic (or multi-period) hub location problem. It proposes a branch-and-bound algorithm that uses a Lagrangian relaxation to obtain lower and upper bounds at the nodes of the tree. The Lagrangian function exploits the structure of the problem and can be decomposed into smaller subproblems that can be solved efficiently. In addition, some reduction procedures based on the Lagrangian bounds are implemented. These yield a considerable reduction of the size of the problem and thus help reduce the computational burden. Numerical results on a set of instances with up to 100 nodes and 10 time periods are reported.