in the future wireless networks, network function virtualization will lay the foun- dation for establishing a new resource management framework to e ciently utilize network resources. the rst part of this thesis deals in the minimization of the to- tal latency for a network and how to solve it e ciently. a model of users, virtual network functions (vnfs) and hosting devices have been considered and was used to nd the minimum latency using integer linear programming (ilp). the problem is np-hard and takes exponential time to solve in the worst case. a stable matching based heuristic has been proposed to solve the problem in polynomial time and then the local search is utilized to improve the e ciency of the result. the second part of this thesis proposes the problem of fair allocation of the vnfs to hosting devices. a mathematical programming based model (ilp) has been designed to solve the problem which takes exponential time to solve in the worst case, due to its np-hard nature. thus an heuristic approach has been provided to solve the problem in polynomial time.