There is a natural shift action defined on multipartitions and their associated multisets of residues. Two different multipartitions may have the same associated residues multiset, thus the orbit cardinality of a multipartition is always greater than or equal to the orbit cardinality of the associated residues multiset. Conversely, a given residues multiset is always associated to a multipartition with the same orbit cardinality. Using the abacus representation of a partition, we will see how the proof reduces to an integer quadratic optimisation problem