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):
This is the cost matrix.
| 76 | 87 | 13 | 30 |
| 66 | 48 | 16 | 42 |
| 43 | 8 | 1 | 37 |
| 85 | 33 | 49 | 64 |
For each row, the minimum element is subtracted from all elements in that row.
| 63 | 74 | 0 | 17 | (-13) |
| 50 | 32 | 0 | 26 | (-16) |
| 42 | 7 | 0 | 36 | (-1) |
| 52 | 0 | 16 | 31 | (-33) |
For each column, the minimum element is subtracted from all elements in that column.
| 21 | 74 | 0 | 0 |
| 8 | 32 | 0 | 9 |
| 0 | 7 | 0 | 19 |
| 10 | 0 | 16 | 14 |
| (-42) | (-17) |
A total of 4 lines are 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 |
Because there are 4 lines required, an optimal assignment exists among the zeros.
| 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 total minimum cost is 122.