A new mixed-integer programming formulation for the maximally diverse grouping problem with attribute values

The paper presents a new mixed-integer programming formulation for the maximally diverse grouping problem (MDGP) with attribute values. The MDGP is the problem of assigning items to groups such that all groups are as heterogeneous as possible. In the version with attribute values, the heterogeneity of groups is measured by the sum of pairwise absolute differences of the attribute values of the assigned items, i.e. by the Manhattan metric. The advantage of the version with attribute values is that the objective function can be reformulated such that it is linear instead of quadratic like in the standard MDGP formulation. We evaluate the new model formulation for the MDGP with attribute values in comparison with two different MDGP formulations from the literature. Our model formulation leads to substantially improved computation times and solves instances of realistic sizes (for example the assignment of students to seminars) with up to 70 items and three attributes, 50 items and five attributes, and 30 items and ten attributes to (near) optimality within half an hour.