Balanced Constrained Partitioning of Distinct Objects

Partition is the process of dividing η elements of a set into ν non-empty subsets where every element is included in exactly one subset. Set partitioning problems play an important role in real-world scenarios such as scheduling, management and grouping. In this paper, n distinct objects are arranged into different groups and the problem of partition is evaluated concerning a people assignment problem of a multi-site company. New constraints such as minimum and the maximum number of people in a single-site company (respectively m and M) that are fixed for all sites are introduced and the solutions for the partition problem for the constraints are also established.