Abstarct: In the network location problem the aim is to determine the optimum location facilities on the Network. This work will be done by providing algorithms for solving these problems. the proposed algorithms, the algorithm that with less time and less cost is more applicable. The P-median problem is one of important problem in location theory and have many applications in various fields such as locating distribution centers, office centers. Lagrangean Relaxation is one of the first methods for solving location problems. Lagrangean relaxation is in fact a way to solve problems in operations research. In this thesis, we analyze the implications of the theory of location problem. In the first chapter, a series of basic concepts and definitions and theorems of the concept of Relaxation is expressed. In Second chapter, we define the problem of simple plant location problem, We provide lower bound for the optimal solution to this problem. In chapter three, the lower bound p-median problem gain with expresion a heuristic algorithm. In the final chapter, Lagrangean methods, and heuristic Surrogate-Lagrangean examined to solve the p-median problem and compared their results.