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:

6912211
1377686
76432240
14423215

Subtract row minima

We subtract the row minimum from each row:

085165(-6)
771080(-6)
5421018(-22)
028181(-14)

Subtract column minima

We subtract the column minimum from each column:

064164
750079
540017
07180
(-21)(-1)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

064164  x
750079  x
540017  x
07180  x

The optimal assignment

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

064164
750079
540017
07180

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

6912211
1377686
76432240
14423215

The optimal value equals 70.