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:
55 | 19 | 65 | 29 |
80 | 84 | 48 | 45 |
56 | 44 | 85 | 19 |
86 | 87 | 92 | 71 |
Subtract row minima
We subtract the row minimum from each row:
36 | 0 | 46 | 10 | (-19) |
35 | 39 | 3 | 0 | (-45) |
37 | 25 | 66 | 0 | (-19) |
15 | 16 | 21 | 0 | (-71) |
Subtract column minima
We subtract the column minimum from each column:
21 | 0 | 43 | 10 |
20 | 39 | 0 | 0 |
22 | 25 | 63 | 0 |
0 | 16 | 18 | 0 |
(-15) | (-3) |
Cover all zeros with a minimum number of lines
There are 4 lines required to cover all zeros:
21 | 0 | 43 | 10 | x |
20 | 39 | 0 | 0 | x |
22 | 25 | 63 | 0 | x |
0 | 16 | 18 | 0 | x |
The optimal assignment
Because there are 4 lines required, the zeros cover an optimal assignment:
21 | 0 | 43 | 10 |
20 | 39 | 0 | 0 |
22 | 25 | 63 | 0 |
0 | 16 | 18 | 0 |
This corresponds to the following optimal assignment in the original cost matrix:
55 | 19 | 65 | 29 |
80 | 84 | 48 | 45 |
56 | 44 | 85 | 19 |
86 | 87 | 92 | 71 |
The optimal value equals 172.
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