The concept of net zero energy buildings (Net ZEB) has received increased attention throughout the last years. A well adapted and optimized design of the energy supply system is crucial for the performance of these buildings. To achieve this, a holistic approach is needed which accounts for the interdependencies between the different supply technologies as well as the construction energy of the installations, consumption profiles and on-site energy resource availability. This paper aims at developing such a model for the optimal sizing of renewable energy supply systems (RES) for residential Net ZEB's involving on-site production of heat and electricity in combination with electricity exchanged with the public grid. The model is based on linear programming and determines the optimal capacities for each relevant supply technology in terms of the overall system costs. It has been successfully applied in a case study. The approach can easily be extended to all kind of RES technologies and also allows for implementing further constraints and requirements proprietary to residential Net ZEBs such as e.g. reliabilities, noise levels or space requirements of relevant technologies.