Solve an assignment problem online

Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given.

Fill in the cost matrix (random cost matrix):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

22859963
96616598
15151592
91601691

Subtract row minima

We subtract the row minimum from each row:

0637741(-22)
350437(-61)
00077(-15)
7544075(-16)

Subtract column minima

We subtract the column minimum from each column:

063774
35040
00040
7544038
(-37)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

063774  x
35040  x
00040  x
7544038  x

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

063774
35040
00040
7544038

This corresponds to the following optimal assignment in the original cost matrix:

22859963
96616598
15151592
91601691

The optimal value equals 151.