Increasing number of devices demand for low latency and high-speed data transmission require that the computation resources to be closer to users. The emerging Mobile Edge Computing (MEC) technology aims to bring the advantages of cloud computing which are computation, storage and networking capabilities in close proximity of user. MEC servers are also integrated with cloud servers which give them flexibility of reaching vast computational power whenever needed. In this thesis, leveraging the idea of Mobile Edge Computing, we propose algorithms for cost-efficient and energy-efficient the placement of Mobile Edge nodes. We focus on uplink energy-efficiency which is essential for certain applications including augmented reality and connected vehicles, as well as extending battery life of user equipment that is favorable for all applications. The experimental results show that our proposed schemes significantly reduce the uplink energy of devices and minimizes the number of edge nodes required in the network.