Solve an assignment problem online

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):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

45534660
93321246
1255957
2489417

Subtract row minima

We subtract the row minimum from each row:

08115(-45)
8120034(-12)
705452(-5)
2085013(-4)

Subtract column minima

We subtract the column minimum from each column:

0812
8120021
705439
208500
(-13)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0812  x
8120021  x
705439  x
208500  x

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

0812
8120021
705439
208500

This corresponds to the following optimal assignment in the original cost matrix:

45534660
93321246
1255957
2489417

The optimal value equals 79.