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:

1711064
5671814
3634261
82109013

Subtract row minima

We subtract the row minimum from each row:

160963(-1)
5267770(-4)
3432059(-2)
720803(-10)

Subtract column minima

We subtract the column minimum from each column:

00963
3667770
1832059
560803
(-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

00963  x
3667770  x
1832059  x
560803  x

The optimal assignment

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

00963
3667770
1832059
560803

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

1711064
5671814
3634261
82109013

The optimal value equals 33.