The models proposed in this thesis are based on two fundamentally different but equally central approaches. The first approach builds on traditionally popular integer programming formulation in facility location theory, in which two such models presented in this thesis. The first one assumes that there are a number of dedicated production technologies for each product whereas, the second one assumes that a set of flexible technologies is also present. Analytical properties of the models are described, which lead to the development of exact and heuristic solution procedures. Results of several sets of computational experiments are also reported. The second approach is based on continuous approximation (also known as continuum mechanics), which has not been used to its potential in the literature. The third model in this thesis is proposed for a system with single product. It is based on the use of continuous functions in representing spatial distribution of cost parameters and decision variables. In this model, the focus is to compute the service regions leaving the precise plant locations to a subsequent analysis. This model lends itself to closed form solutions and allows derivation of a number of insights on the impact of several cost factors on facility design decisions. Then, it is utilized in an analytical framework to analyze several plant focus decisions of firms in a multi-product environment. The closed form solution is used to analyze several product and market focus strategies, which have provided several insights into more sophisticated plant focus decisions and into the impact of different production technologies on these decisions.