This book contributes to several Operations Research fields, namely, global optimization, multiobjective optimization and location science. Reliable methods both for single and bi-objective optimization problems are developed. They are branch-and-bound algorithms which make use of interval analysis tools. Thus, they can be applied to (nearly) any optimization problem. To prove their applicability, new planar competitive facility location problems introduced in this book have been solved with them. Competitive location deals with the problem of locating facilities to provide goods to the consumers of a given geographical area where other competing facilities offering the same goods are already present or will enter the market in the near future. In the new location models in this book, both the location and the quality (design) of the new facilities are to be found. The present volume is addressed to researchers and other professionals from the fields of operations research, management science, computer science and applied mathematics. It may also be used in graduated courses to show how mathematical programming can be applied to real situations.