On the way to meet the internationally sanctioned climate targets, zero emission buildings / zero energy buildings (ZEB) will be an important step. Research is ongoing on what a reasonable definition of ZEB will contain. In Norway, it is decided that the building code should be nearly zero energy buildings from the year 2020. In this master’s thesis, an optimization model for finding cost-optimal investment and operational strategies for ZEB is developed. The building modelled, is a passive school with a hydronic heat distribution system. Possible investments include photovoltaic solar cells (PV), solar collectors, heat pumps, biomass boilers, electric boiler, heat storage and connection to the district heating grid. The model is designed as a dynamic mixed integer programming model, and implemented in Mosel Xpress. The model minimizes the total discounted costs of operations and investments over the lifetime of the building. Different restrictions of zero CO2 emissions, zero primary energy consumption and level of grid burden can be applied. The analysis shows that if a zero CO2 restriction with Norwegian CO2 factors are applied, the least expensive way to reach ZEB is by investing in PV in combination with pellet biomass boiler as base load and district heating to cover peak demand. To reach the zero balance for the school with Norwegian CO2 factors, the highest hourly value for export of electricity per hour exceeds the maximum hourly value of imports by about 120%. If European factors for CO2 is applied, it will be more reasonable to reach ZEB than with Norwegian factors. If asymmetric primary energy factors are used instead of symmetric factors, investment in PV becomes higher, and the peak export values increases. The model is developed as a deterministic model, and does not take into account uncertainties in input data. To compensate for this, various sensitivity analyses are conducted. Future work includes testing the model with load profiles for other types of buildings.