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
This is the original cost matrix:
19 | 93 | 28 |
63 | 84 | 40 |
74 | 99 | 31 |
Subtract row minima
We subtract the row minimum from each row:
0 | 74 | 9 | (-19) |
23 | 44 | 0 | (-40) |
43 | 68 | 0 | (-31) |
Subtract column minima
We subtract the column minimum from each column:
0 | 30 | 9 |
23 | 0 | 0 |
43 | 24 | 0 |
(-44) |
Cover all zeros with a minimum number of lines
There are 3 lines required to cover all zeros:
0 | 30 | 9 | x |
23 | 0 | 0 | x |
43 | 24 | 0 | x |
The optimal assignment
Because there are 3 lines required, the zeros cover an optimal assignment:
0 | 30 | 9 |
23 | 0 | 0 |
43 | 24 | 0 |
This corresponds to the following optimal assignment in the original cost matrix:
19 | 93 | 28 |
63 | 84 | 40 |
74 | 99 | 31 |
The optimal value equals 134.
HungarianAlgorithm.com © 2013-2025