Multi-fair Capacitated Students-Topics Grouping Problem

Group work is a prevalent activity in educational settings, where students are often divided into topic-specific groups based on their preferences. The grouping should reflect students’ aspirations as much as possible. Usually, the resulting groups should also be balanced in terms of protected attributes like gender, as studies suggest that students may learn better in mixed-gender groups. Moreover, to allow a fair workload across the groups, the cardinalities of the different groups should be balanced. In this paper, we introduce a multi-fair capacitated (MFC) grouping problem that fairly partitions students into non-overlapping groups while ensuring balanced group cardinalities (with a lower and an upper bound), and maximizing the diversity of members regarding the protected attribute. To obtain the MFC grouping, we propose three approaches: a greedy heuristic approach, a knapsack-based approach using vanilla maximal knapsack formulation, and an MFC knapsack approach based on group fairness knapsack formulation. Experimental results on a real dataset and a semi-synthetic dataset show that our proposed methods can satisfy students’ preferences and deliver balanced and diverse groups regarding cardinality and the protected attribute, respectively.