Abstarct: Location theory is an important field of the operations research and has many applications in the real world. In recent years, some new versions of the facility location models, called improvement facility location, involves the inverse location, backup facility location, balanced facility location and goal location models, have found an increasing interest. In this thesis some improvement p-median problems are considered. Efficient methods baxsed on some properties of the desirable and undesirable backup 2-median problems on a tree and the multi-facility backup goal location problem in continuous space are presented. Moreover, the inverse models of the backup 2-median problem with minimum cost and limited budgeting in discrete and continuous space are considered. The Wiszfeld like, particle swarm optimization and cultural optimization algorithms are used to solve the inverse models. Finally, two O(n log n) algorithms are presented for solving the inverse and reverse balanced 2-median problems.