This paper describes an exact algorithm capable of solving large-scale instances of the well-known uncapacitated hub location problem with multiple assignments. The algorithm applies Benders decomposition to a strong path-based formulation of the problem. The standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a multicut reformulation, the generation of strong optimality cuts, the integration of reduction tests, and the execution of a heuristic procedure. Extensive computational experiments were performed to evaluate the efficiency and robustness of the algorithm. Computational results obtained on classical benchmark instances (with up to 200 nodes) and on a new and more difficult set of instances (with up to 500 nodes) confirm the efficiency of the algorithm.

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This paper presents a dynamic (or multi-period) hub location problem. It proposes a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the tree. The Lagrangean function exploits the structure of the problem and can be decomposed into smaller subproblems which can be solved efficiently. In addition, some reduction procedures based on the Lagrangean 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 battery of instances with up to 100 nodes and 10 time periods are reported.

This paper presents a class of hub network design problems with profit-oriented objectives, which extend several families of classical hub location problems. Potential applications arise in the design of air and ground transportation networks. These problems include decisions on the origin/destination nodes that will be served as well as the activation of different types of edges, and consider the simultaneous optimization of the collected profit, setup cost of the hub network and transportation cost. Alternative models and integer programming formulations are proposed and analyzed. Results from computational experiments show the complexity of such models and highlight their superiority for decision-making.Peer ReviewedPostprint (author's final draft

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We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field.