District heating is used in many urban areas in Sweden. Almost always, the district heating utility is owned by the municipality and the municipality naturally encourages proprietors to connect their buildings to the grid, even if they cannot really force them to do so. The building owners are free to choose the best system, i.e. the cheapest one, for their need. Unfortunately, it is not always so easy to find the best solution. Mixed integer linear programming (MLIP) models might here come to help. By such computer programs it is possible to find the absolutely cheapest system of available alternatives, or even combinations among them. This paper shows how to design such a model and further how to closely depict the district heating, and electricity tariff. This is of course very important because the only interface between the proprietor of the building and the utility is found in this bureaucratic instrument. If the tariff is too high the building owners will choose other heating systems than district heating, or even worse, combining district heating with alternative base load sources. In Sweden, this has been of interest because ground-water coupled heat pumps can be profitable, operated by use of the relatively low electricity prices. In this paper we show that dual-fuel, and sometimes even triple-fuel systems, are of interest when the proprietor aims at minimising the cost for space and domestic hot-water heating. © 2008 Elsevier B.V. All rights reserved.