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.
| 73 | 74 | 6 | 56 |
| 31 | 15 | 83 | 3 |
| 10 | 18 | 97 | 71 |
| 17 | 55 | 43 | 29 |
For each row, the minimum element is subtracted from all elements in that row.
| 67 | 68 | 0 | 50 | (-6) |
| 28 | 12 | 80 | 0 | (-3) |
| 0 | 8 | 87 | 61 | (-10) |
| 0 | 38 | 26 | 12 | (-17) |
For each column, the minimum element is subtracted from all elements in that column.
| 67 | 60 | 0 | 50 |
| 28 | 4 | 80 | 0 |
| 0 | 0 | 87 | 61 |
| 0 | 30 | 26 | 12 |
| (-8) |
A total of 4 lines are required to cover all zeros.
| 67 | 60 | 0 | 50 | x |
| 28 | 4 | 80 | 0 | x |
| 0 | 0 | 87 | 61 | x |
| 0 | 30 | 26 | 12 | x |
Because there are 4 lines required, an optimal assignment exists among the zeros.
| 67 | 60 | 0 | 50 |
| 28 | 4 | 80 | 0 |
| 0 | 0 | 87 | 61 |
| 0 | 30 | 26 | 12 |
This corresponds to the following optimal assignment in the original cost matrix.
| 73 | 74 | 6 | 56 |
| 31 | 15 | 83 | 3 |
| 10 | 18 | 97 | 71 |
| 17 | 55 | 43 | 29 |
The total minimum cost is 44.