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.
| 96 | 91 | 48 |
| 94 | 47 | 58 |
| 7 | 64 | 45 |
For each row, the minimum element is subtracted from all elements in that row.
| 48 | 43 | 0 | (-48) |
| 47 | 0 | 11 | (-47) |
| 0 | 57 | 38 | (-7) |
Because each column already contains a zero, subtracting the column minima has no effect.
A total of 3 lines are required to cover all zeros.
| 48 | 43 | 0 | x |
| 47 | 0 | 11 | x |
| 0 | 57 | 38 | x |
Because there are 3 lines required, an optimal assignment exists among the zeros.
| 48 | 43 | 0 |
| 47 | 0 | 11 |
| 0 | 57 | 38 |
This corresponds to the following optimal assignment in the original cost matrix.
| 96 | 91 | 48 |
| 94 | 47 | 58 |
| 7 | 64 | 45 |
The total minimum cost is 102.