Man-made and natural disasters have been affecting an increasing number of people in recent years. This trend is expected to continue as the number and size coastal settlements grow, forcing humanitarian organisations to seek cost-effective solutions to improve response operations.

In recent years, Unmanned Aerial Vehicles have been increasingly deployed in humanitarian response as they provide an economical solution to the numerous challenges of post-disaster land-based relief operations, including the presence of partial or complete damage to the transport infrastructure, or absence thereof. In addition to some regulatory constraints, vehicle range and integration with the existing response mechanisms remain as key limitations to their deployment in practice. Therefore, it is imperative to develop a quantitative framework capable of determining the optimal strategy for UAV-based humanitarian response. This thesis proposes novel methodologies to use UAVs in relief distribution operations.

A method for routing UAVs and locating supporting infrastructure necessary to deliver relief cargo is developed. A trajectory management process is proposed to represent UAV behaviour during cruise flight accurately. Building on this, we also study the relationship between payload and energy consumption. An endogenous stochastic model is developed to assess network damage and inform the routing of ground vehicles.

The algorithms are applied on a dataset drawn from the earthquake responses in Taiwan after the Chi-Chi earthquake of 1999 and Port-au-Prince after the Haiti earthquake in 2010. Results show that UAVs can be used as a means of transportation for relief during the first days of a disaster, with close to 20,000 kg of cargo transported in 35 hours. The approach developed provides up to 40\% improvements in terms of mission duration compared to well-established methods. By assisting trucks through network assessment, UAVs provide vehicle travel times by up to 20\% depending on the network damage levels. These results indicate that fleets of small UAVs can provide significant benefits to humanitarian response.