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.
| 3 | 2 | 1 |
| 12 | 23 | 23 |
| 123 | 23 | 12 |
For each row, the minimum element is subtracted from all elements in that row.
| 2 | 1 | 0 | (-1) |
| 0 | 11 | 11 | (-12) |
| 111 | 11 | 0 | (-12) |
For each column, the minimum element is subtracted from all elements in that column.
| 2 | 0 | 0 |
| 0 | 10 | 11 |
| 111 | 10 | 0 |
| (-1) |
A total of 3 lines are required to cover all zeros.
| 2 | 0 | 0 | x |
| 0 | 10 | 11 | x |
| 111 | 10 | 0 | x |
Because there are 3 lines required, an optimal assignment exists among the zeros.
| 2 | 0 | 0 |
| 0 | 10 | 11 |
| 111 | 10 | 0 |
This corresponds to the following optimal assignment in the original cost matrix.
| 3 | 2 | 1 |
| 12 | 23 | 23 |
| 123 | 23 | 12 |
The total minimum cost is 26.