Abstract

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems.