The assignment problem is classified into
balanced assignment problem and 
unbalanced assignment problem.

If the number of rows is equal to the number of columns, then the problem is termed as a balanced assignment problem;

otherwise, an unbalanced assignment problem.
If the problem is unbalanced, like an unbalanced transportation problem, then necessary number of dummy row(s)/column(s) is added
such that the cost matrix is a square matrix.
The values for the entries in the dummy row(s)/column(s) are assumed to be zero.
Under such a condition, while implementing the solution, the dummy row(s) or the dummy column(s) will not have assignment(s).