This thesis focuses on deriving exact methods to place controllers on a network for the planning problem of Software Defined Network (SDN). A first mathematical model, referred to as the planning model, is proposed that decides the optimal location to place controllers on a network while minimizing the overall cost. A second mathe- matical model, referred to as the expansion model, is proposed that determines the changes to optimally place controllers on an existing SDN network. The advantages of the proposed models are to incorporate realistic constrains. In the planning problem, as the
input size increased, the time to find the optimal solution also increased in non-polynomial time. The expansion problem results show that changes can be made to existing implementations by altering many of the input variables. The expansion model allows control of how much of the existing network changes