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:
1 | 5 | 3 |
4 | 2 | 8 |
7 | 9 | 3 |
Subtract row minima
We subtract the row minimum from each row:
0 | 4 | 2 | (-1) |
2 | 0 | 6 | (-2) |
4 | 6 | 0 | (-3) |
Subtract column minima
Because each column contains a zero, subtracting column minima has no effect.
Cover all zeros with a minimum number of lines
There are 3 lines required to cover all zeros:
0 | 4 | 2 | x |
2 | 0 | 6 | x |
4 | 6 | 0 | x |
The optimal assignment
Because there are 3 lines required, the zeros cover an optimal assignment:
0 | 4 | 2 |
2 | 0 | 6 |
4 | 6 | 0 |
This corresponds to the following optimal assignment in the original cost matrix:
1 | 5 | 3 |
4 | 2 | 8 |
7 | 9 | 3 |
The optimal value equals 6.
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