Question

Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance traveled is minimized. The matrix below shows the distance.

Answer 1

Here the number of trucks is 4 and vacant spaces are 6. So the given assignment problem is the unbalanced problem. So we introduce two dummy columns with all the entries zero to make is balanced. So the problem is

Here only 4 vacant spaces can be assigned to four trucks 

Step 1: Not necessary since all rows have zeros. 

Step 2:

Step 3: (Assignment)

The optimal assignment schedule and total distance travelled is

Thus the minimum distance travelled is 12 km.