Intensity modulated radiation therapy (IMRT) can be very effective in the treatment of primary tumours. The challenge in therapy planning is to develop treatment plans that allow effective treatment of the tumour while at the same time limiting the radiation dose to surrounding tissue and organs at risk. We present a mathematical model of inverse planning for IMRT. The task of such a tool is to identify an optimal treatment plan, which consists of the irradiation directions and intensity profiles to achieve a high dose in the target volume (tumour) while at the same time protecting organs at risk from dangerous high doses. To optimise intensity profiles and beam directions we consider underdosing the tumour and overdosing any organ at risk as objectives to be minimised simultaneously. Our model allows the incorporation of optimisation of irradiation directions. This yields a multicriteria integer model of the problem. This model has a (possibly very large) set of efficient solutions, from which a representative subset is calculated and stored in a database. An efficient solution is one in which neither the results for the target volume nor for the organs at risk can be improved without deteriorating the results for another volume of interest. We propose an interactive tool that allows the online selection of a plan through the use of the pre-computed database of efficient solutions. The proposed model and methodology has considerable advantages over existing software packages and we expect it to improve quality of treatment plans while at the same time reducing planning time. We present some results from 2D-prototype software.