In this project, we consider problems arising in facility location analysis and we will provide efficient algorithmical solutions to them. Whenever facilities have to be placed or removed, we can search for a model to quantitatively measure the impact of the decision, and the best decision translates into an optimization problem. The functions to optimize may be simple ones, but in most real applications we have to deal with a trade-off between different criteria. When we aim to efficient algorithms for solving these different problems, the algorithms need be tailored to each particular problem, and different problems call for drastically different algorithmical solutions. The techniques to be used in our project will be mainly drawn from the fields of computational geometry, graph algorithms and data structures. The interaction between these fields and location analysis has proven and keeps being successful.