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:

1651991
14827481
19789955
82708825

Subtract row minima

We subtract the row minimum from each row:

1550980(-1)
0686067(-14)
0598036(-19)
5745630(-25)

Subtract column minima

We subtract the column minimum from each column:

155380
023067
0142036
57030
(-45)(-60)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

155380  x
023067  x
0142036  x
57030  x

The optimal assignment

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

155380
023067
0142036
57030

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

1651991
14827481
19789955
82708825

The optimal value equals 164.