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:

57725580
4126625
23313073
35485396

Subtract row minima

We subtract the row minimum from each row:

217025(-55)
3520019(-6)
08750(-23)
0131861(-35)

Subtract column minima

We subtract the column minimum from each column:

2906
351200
00731
051842
(-8)(-19)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

2906  x
351200  x
00731  x
051842  x

The optimal assignment

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

2906
351200
00731
051842

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

57725580
4126625
23313073
35485396

The optimal value equals 146.