The optimal heating-system-retrofit strategy for existing buildings differs due to varying prices of energy, building and installation features, climate conditions, etc. We have examined a test building situated in Linkoping, Sweden. By using the OPERA model, we were able to arrive at the optimal retrofit strategy, which includes a ground-coupled heat pump using electricity to run the compressor. Unfortunately, the price of electricity differs according to the time of day, month, etc. These variations are not included in the OPERA model. In OPERA, the price should be divided into 12 segments, one for each month of the year since climate data are divided in this manner. Fine tuning of a dual-fuel system (an oil-fired boiler handles the peak load and a heat pump the base thermal load) is optimized using the Mixed Integer Linear Programming (MILP) method. Adding a hot-water accumulator also makes it possible to use low electricity prices for space and domestic hot-water heating. This system competes in the model with traditional heating devices such as district heating. The optimal method of heating the building was found for using the heat pump alone.