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.
| 22 | 1 | 78 |
| 42 | 48 | 6 |
| 38 | 84 | 34 |
For each row, the minimum element is subtracted from all elements in that row.
| 21 | 0 | 77 | (-1) |
| 36 | 42 | 0 | (-6) |
| 4 | 50 | 0 | (-34) |
For each column, the minimum element is subtracted from all elements in that column.
| 17 | 0 | 77 |
| 32 | 42 | 0 |
| 0 | 50 | 0 |
| (-4) |
A total of 3 lines are required to cover all zeros.
| 17 | 0 | 77 | x |
| 32 | 42 | 0 | x |
| 0 | 50 | 0 | x |
Because there are 3 lines required, an optimal assignment exists among the zeros.
| 17 | 0 | 77 |
| 32 | 42 | 0 |
| 0 | 50 | 0 |
This corresponds to the following optimal assignment in the original cost matrix.
| 22 | 1 | 78 |
| 42 | 48 | 6 |
| 38 | 84 | 34 |
The total minimum cost is 45.