In this paper, the energy efficiency of edge computing platforms for IoT networks connected to a passive optical network (PON) is investigated. We have developed a mixed integer linear programming (MILP) optimization model, which optimizes the placement and number of the cloudlets and VMs and utilizes energy efficient routes with the objective of minimizing the total IoT network and processing power consumption. Our results show that the power consumption can be reduced by consolidating the placement of these VMs at the PON Optical Line Terminal (OLT) in cases where the traffic volume is still high after data processing, ie at low traffic reduction percentages. On the other hand, at high traffic reduction ratios, better power efficiency can be accomplished by placing VMs in lower layer nodes (relays). Our results indicate that utilizing PONs and serving heterogeneous VMs can save up to 19% of the total power. Based on the MILP model insights, a heuristic is developed with very comparable MILP-heuristic power consumption values. We considered three scenarios that represent different levels of homogeneous and heterogeneous VM CPU demands. Good agreement was observed between the heuristic results (17% power saving) and the MILP which results in 19% power saving.