The balanced maximally diverse grouping problem with block constraints

Abstract

Abstract The paper investigates the assignment of items to groups such that all groups are balanced, i.e. all groups contain the same number of items and all pairs of groups are as homogeneous as possible regarding the attribute values of the assigned items. Therefore, we adapt the maximally diverse grouping problem (MDGP). It is especially known in the context of students being assigned to groups. We describe the set of optimal solutions for the MDGP for realistic input data and develop a new linear objective function to determine the best balanced solution amongst all optimal solutions for the MDGP by weighting the biggest diversity between two groups with a higher value than the second biggest and so on. Furthermore, an integer program, a detailed complexity analysis, and a computational study are presented.