The balanced maximally diverse grouping problem with integer attribute values

Abstract The paper considers the assignment of items to groups according their attribute values such that are as balanced possible. Although problem is in general NP -hard, we prove it can be solved pseudo-polynomial time if integer. We point out a relation partition and more multi-way number partitioning. Furthermore, introduce mixed-integer programming (MIP) formulation, variable reduction technique, an efficient lower bound for objective value. Our computational results show meets optimal value most our instances realistic size. Hence, MIP solves with several thousand within seconds optimality.