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.
| 92 | 78 | 32 | 44 |
| 18 | 42 | 49 | 75 |
| 66 | 98 | 73 | 52 |
| 3 | 71 | 4 | 23 |
For each row, the minimum element is subtracted from all elements in that row.
| 60 | 46 | 0 | 12 | (-32) |
| 0 | 24 | 31 | 57 | (-18) |
| 14 | 46 | 21 | 0 | (-52) |
| 0 | 68 | 1 | 20 | (-3) |
For each column, the minimum element is subtracted from all elements in that column.
| 60 | 22 | 0 | 12 |
| 0 | 0 | 31 | 57 |
| 14 | 22 | 21 | 0 |
| 0 | 44 | 1 | 20 |
| (-24) |
A total of 4 lines are required to cover all zeros.
| 60 | 22 | 0 | 12 | x |
| 0 | 0 | 31 | 57 | x |
| 14 | 22 | 21 | 0 | x |
| 0 | 44 | 1 | 20 | x |
Because there are 4 lines required, an optimal assignment exists among the zeros.
| 60 | 22 | 0 | 12 |
| 0 | 0 | 31 | 57 |
| 14 | 22 | 21 | 0 |
| 0 | 44 | 1 | 20 |
This corresponds to the following optimal assignment in the original cost matrix.
| 92 | 78 | 32 | 44 |
| 18 | 42 | 49 | 75 |
| 66 | 98 | 73 | 52 |
| 3 | 71 | 4 | 23 |
The total minimum cost is 129.