Relay location in telecommunications and transportation networks

With di↵erent names and functions, relays play a crucial role in the design of telecommunications and transportation networks and finding optimal relay locations is an important concern in various applications. We investigate several relay location problems from the literature, propose new ones and design efficient solution methods to obtain managerial insights. The basic problem we investigate in this dissertation is the Regenerator Location Problem (RLP). We revisit RLP from the hub location perspective and introduce two new dimensions involving the challenges of survivability. Considering the flexible optical network architecture, we relax all pairs connectivity, infinite capacity links and single modulation level assumptions of RLP and introduce the regenerator location problem in flexible optical networks (RLP-FON). RLP-FON solves regenerator location, routing, bandwidth allocation and modulation selection problems jointly to better exploit the opportunities o↵ered by this novel network architecture. For various problems arising in telecommunications and transportation it is beneficial to consider edge design and relay locations together. We add the edge design aspect to RLP and extend our research to Network Design Problem with Relays. Di↵erent than telecommunications networks, the total length of a route is an important issue in transportation. So in the final part we include circuitry constraints to the routing decisions and study the Refueling Station Location Problem for Alternative Fuel Vehicles. We approach relay location problems from di↵erent angles: network topologies, capacities, costs, and demands and provide significant theoretical results. For all relay location problems, the reach limitations for the related entities pose the main challenge and we propose novel path-segment based formulation approaches to incorporate these constraints in an efficient way. Extensive numerical experiments with realistic problem instances attest to the efficacy of the proposed approach.