Network Functions Virtualization (NFV) has been revolutionizing and improving the way networking services are deployed but also requires the dynamic scaling of resources during the lifecycle management of Virtual Network Functions (VNFs) with increasing service demand. We propose an Integer Linear Programming (ILP) approach and a Greedy heuristic to address this NP-Hard scaling problem. Both horizontal (scale out/in) and vertical (scale up/down) scaling are considered and the scalability of the ILP is addressed by reducing the number of candidate hosts in the search space. Extensive simulations evaluate the performance of the algorithms in successful scalings and VNF migrations and highlight the importance of using the algorithms to tidy up the infrastructure to accept more users. The results show that the ILP can outperform the Greedy heuristic if appropriate actions are selected.