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.
| 21 | 47 | 10 |
| 49 | 94 | 96 |
| 65 | 6 | 16 |
For each row, the minimum element is subtracted from all elements in that row.
| 11 | 37 | 0 | (-10) |
| 0 | 45 | 47 | (-49) |
| 59 | 0 | 10 | (-6) |
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.
| 11 | 37 | 0 | x |
| 0 | 45 | 47 | x |
| 59 | 0 | 10 | x |
Because there are 3 lines required, an optimal assignment exists among the zeros.
| 11 | 37 | 0 |
| 0 | 45 | 47 |
| 59 | 0 | 10 |
This corresponds to the following optimal assignment in the original cost matrix.
| 21 | 47 | 10 |
| 49 | 94 | 96 |
| 65 | 6 | 16 |
The total minimum cost is 65.