Mathematical programming for nominating exchange students for international universities: The impact of stakeholders’ objectives and fairness constraints on allocations

We consider the problem of nominating exchange students to attend international universities where places are limited. We take into account three objectives: The sending university aims to maximize the number of nominations, the students seek nomination for a highly preferred university and, finally, the receiving universities strive for excellent incoming students. Pairwise comparison of students should guarantee the following fairness: A student with higher academic achievements should be preferred over a student with lower academic achievements. We provide mathematical programming models of the nomination problem which maximize the overall objectives and guarantee different types of pairwise fairness. Several years of real data from a major school are employed to evaluate the models’ performance including a benchmark against the heuristic that is used by the school. We show analytically and experimentally that the heuristic approach fails to guarantee some pairwise fairness. Our results reveal the following four insights: First, compared to the current approach, up to 6.6% more students can be nominated with our optimization model while ensuring all pairwise fairness perspectives. Second, on average, students are nominated with better academic achievements. Third, the problem instances can be solved to optimality within a fraction of a second even for large-size instances comprising more than 500 students and about 150 schools offering nearly 450 exchange places. This is important for its use in practice. Last, up to 17.9% more students can be nominated when considering the overall objective to maximize nominations.