This study presents a two-phase binary-goal programming-based approach for solving a novel system design project-team formation problem which involves several restrictions and requirements as well as the preferences of the potential team members. The problem instance considered in this study basically includes two types of allocations, as the allocations of students and academic advisers, which are performed in the first and second phase of the proposed solution approach, respectively. Although it represents a particular case as represented in this study, it can be easily generalised to be used for solving similar project-team formation problems. We implement our methodology on a real-life problem in an academic institution and compare our solutions to the real-life allocations performed manually. It is noted that, in terms of satisfying the goals of the problem, our approach significantly outperforms the real-life allocations. In addition, computational results show our model's ability to solve similar-sized real-life problems in reasonable time periods on an average personal computer, implying its potential for significant savings in terms of the human resources available.