Negative solutions can be avoided with the determination and elimination of surplus assignments. When negative assignments are not permitted, the preliminary transformations may lead to reduced matrices with more assignments to some column (row) than specified by the quotas. The determination of such a surplus also leads to the determination of a transformation. Thus in the matrix C(1) of Table 5 we see that the initial assignments leads to a surplus of one unit in column 2, and to a surplus of one unit in row 4. Considering the surplus in column 2, there must be an additional zero term provided in row 2 or row 3. Here delta = 3, and the subtraction of 3 units from row 2 and row 3, with the subtraction of -3 units from column 2, leads to an increment to the bounding set sum of 3 units and to the completely reduced, matrix C(3). In this case the surplus in column 2, and the surplus in row 4, are fortunately removed at one step. The simple removal of the surplus in row 4 with delta = 1 does not result in the removal of the surplus in column 2. An additional transformation with delta = 2 is needed, as in the formal version shown in Table 5.