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:
76 | 87 | 13 | 30 |
66 | 48 | 16 | 42 |
43 | 8 | 1 | 37 |
85 | 33 | 49 | 64 |
Subtract row minima
We subtract the row minimum from each row:
63 | 74 | 0 | 17 | (-13) |
50 | 32 | 0 | 26 | (-16) |
42 | 7 | 0 | 36 | (-1) |
52 | 0 | 16 | 31 | (-33) |
Subtract column minima
We subtract the column minimum from each column:
21 | 74 | 0 | 0 |
8 | 32 | 0 | 9 |
0 | 7 | 0 | 19 |
10 | 0 | 16 | 14 |
(-42) | (-17) |
Cover all zeros with a minimum number of lines
There are 4 lines required to cover all zeros:
21 | 74 | 0 | 0 | x |
8 | 32 | 0 | 9 | x |
0 | 7 | 0 | 19 | x |
10 | 0 | 16 | 14 | x |
The optimal assignment
Because there are 4 lines required, the zeros cover an optimal assignment:
21 | 74 | 0 | 0 |
8 | 32 | 0 | 9 |
0 | 7 | 0 | 19 |
10 | 0 | 16 | 14 |
This corresponds to the following optimal assignment in the original cost matrix:
76 | 87 | 13 | 30 |
66 | 48 | 16 | 42 |
43 | 8 | 1 | 37 |
85 | 33 | 49 | 64 |
The optimal value equals 122.
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