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.
| 24 | 50 | 61 |
| 42 | 72 | 55 |
| 93 | 53 | 54 |
For each row, the minimum element is subtracted from all elements in that row.
| 0 | 26 | 37 | (-24) |
| 0 | 30 | 13 | (-42) |
| 40 | 0 | 1 | (-53) |
For each column, the minimum element is subtracted from all elements in that column.
| 0 | 26 | 36 |
| 0 | 30 | 12 |
| 40 | 0 | 0 |
| (-1) |
A total of 2 lines are required to cover all zeros.
| 0 | 26 | 36 | |
| 0 | 30 | 12 | |
| 40 | 0 | 0 | x |
| x |
The number of lines is smaller than 3. The smallest uncovered element is 12. We subtract this value from all uncovered elements and add it to all elements covered twice.
| 0 | 14 | 24 |
| 0 | 18 | 0 |
| 52 | 0 | 0 |
A total of 3 lines are required to cover all zeros.
| 0 | 14 | 24 | x |
| 0 | 18 | 0 | x |
| 52 | 0 | 0 | x |
Because there are 3 lines required, an optimal assignment exists among the zeros.
| 0 | 14 | 24 |
| 0 | 18 | 0 |
| 52 | 0 | 0 |
This corresponds to the following optimal assignment in the original cost matrix.
| 24 | 50 | 61 |
| 42 | 72 | 55 |
| 93 | 53 | 54 |
The total minimum cost is 132.