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.
| 97 | 98 | 23 | 64 |
| 25 | 82 | 80 | 87 |
| 49 | 44 | 41 | 4 |
| 84 | 17 | 18 | 94 |
For each row, the minimum element is subtracted from all elements in that row.
| 74 | 75 | 0 | 41 | (-23) |
| 0 | 57 | 55 | 62 | (-25) |
| 45 | 40 | 37 | 0 | (-4) |
| 67 | 0 | 1 | 77 | (-17) |
Because each column already contains a zero, subtracting the column minima has no effect.
A total of 4 lines are required to cover all zeros.
| 74 | 75 | 0 | 41 | x |
| 0 | 57 | 55 | 62 | x |
| 45 | 40 | 37 | 0 | x |
| 67 | 0 | 1 | 77 | x |
Because there are 4 lines required, an optimal assignment exists among the zeros.
| 74 | 75 | 0 | 41 |
| 0 | 57 | 55 | 62 |
| 45 | 40 | 37 | 0 |
| 67 | 0 | 1 | 77 |
This corresponds to the following optimal assignment in the original cost matrix.
| 97 | 98 | 23 | 64 |
| 25 | 82 | 80 | 87 |
| 49 | 44 | 41 | 4 |
| 84 | 17 | 18 | 94 |
The total minimum cost is 69.