In this thesis, we propose an exact model for the planning and design problem of fog networks. The model simultaneously determines the optimal location, the capacity and the number of fog node(s) as well as the interconnection between the installed fog nodes and the cloud, while minimizing the delay in the network and the amount of traffic going to the cloud. To address this multiobjective problem, three multiobjective optimization methods are evaluated. The CPLEX solver was used to optimize the model for the three methods with different problem sizes and the results are analyzed. The results show that, as the input size increases, the delay and the traffic also increase in a linear form; whereas the solution time increases in non-polynomial time. As the model considers realistic edge device traffic parameters and constraints, it can be helpful in deploying fog networks in the current cloud computing architecture.