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.
| 63 | 54 | 57 | 91 |
| 88 | 61 | 68 | 73 |
| 54 | 27 | 30 | 76 |
| 22 | 71 | 53 | 69 |
For each row, the minimum element is subtracted from all elements in that row.
| 9 | 0 | 3 | 37 | (-54) |
| 27 | 0 | 7 | 12 | (-61) |
| 27 | 0 | 3 | 49 | (-27) |
| 0 | 49 | 31 | 47 | (-22) |
For each column, the minimum element is subtracted from all elements in that column.
| 9 | 0 | 0 | 25 |
| 27 | 0 | 4 | 0 |
| 27 | 0 | 0 | 37 |
| 0 | 49 | 28 | 35 |
| (-3) | (-12) |
A total of 4 lines are required to cover all zeros.
| 9 | 0 | 0 | 25 | x |
| 27 | 0 | 4 | 0 | x |
| 27 | 0 | 0 | 37 | x |
| 0 | 49 | 28 | 35 | x |
Because there are 4 lines required, an optimal assignment exists among the zeros.
| 9 | 0 | 0 | 25 |
| 27 | 0 | 4 | 0 |
| 27 | 0 | 0 | 37 |
| 0 | 49 | 28 | 35 |
This corresponds to the following optimal assignment in the original cost matrix.
| 63 | 54 | 57 | 91 |
| 88 | 61 | 68 | 73 |
| 54 | 27 | 30 | 76 |
| 22 | 71 | 53 | 69 |
The total minimum cost is 179.