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:
63 | 54 | 57 | 91 |
88 | 61 | 68 | 73 |
54 | 27 | 30 | 76 |
22 | 71 | 53 | 69 |
Subtract row minima
We subtract the row minimum from each row:
9 | 0 | 3 | 37 | (-54) |
27 | 0 | 7 | 12 | (-61) |
27 | 0 | 3 | 49 | (-27) |
0 | 49 | 31 | 47 | (-22) |
Subtract column minima
We subtract the column minimum from each column:
9 | 0 | 0 | 25 |
27 | 0 | 4 | 0 |
27 | 0 | 0 | 37 |
0 | 49 | 28 | 35 |
(-3) | (-12) |
Cover all zeros with a minimum number of lines
There are 4 lines required to cover all zeros:
9 | 0 | 0 | 25 | x |
27 | 0 | 4 | 0 | x |
27 | 0 | 0 | 37 | x |
0 | 49 | 28 | 35 | x |
The optimal assignment
Because there are 4 lines required, the zeros cover an optimal assignment:
9 | 0 | 0 | 25 |
27 | 0 | 4 | 0 |
27 | 0 | 0 | 37 |
0 | 49 | 28 | 35 |
This corresponds to the following optimal assignment in the original cost matrix:
63 | 54 | 57 | 91 |
88 | 61 | 68 | 73 |
54 | 27 | 30 | 76 |
22 | 71 | 53 | 69 |
The optimal value equals 179.
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