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:

47426026
50786317
71501584
37475931

Subtract row minima

We subtract the row minimum from each row:

2116340(-26)
3361460(-17)
5635069(-15)
616280(-31)

Subtract column minima

We subtract the column minimum from each column:

150340
2745460
5019069
00280
(-6)(-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

150340  x
2745460  x
5019069  x
00280  x

The optimal assignment

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

150340
2745460
5019069
00280

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

47426026
50786317
71501584
37475931

The optimal value equals 111.