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This paper addresses R&D portfolio selection in social institutions, state-owned enterprises, and other nonprofit organizations which periodically launch a call for proposals and distribute funds among accepted projects. A nonlinear discontinuous bicriterion optimization model is developed in order to find a compromise between a portfolio quality measure and the number of projects selected for funding. This model is then transformed into a linear mixed-integer formulation to present the Pareto front. Numerical experiments with up to 25 000 projects competing for funding demonstrate a high computational efficiency of the proposed approach. The acceptance/rejection rules are obtained for a portfolio using the rough set methodology.