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:

77862697
27926662
30319411
17343031

Subtract row minima

We subtract the row minimum from each row:

5160071(-26)
0653935(-27)
1920830(-11)
0171314(-17)

Subtract column minima

We subtract the column minimum from each column:

5143071
0483935
193830
001314
(-17)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

5143071  x
0483935  x
193830  x
001314  x

The optimal assignment

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

5143071
0483935
193830
001314

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

77862697
27926662
30319411
17343031

The optimal value equals 98.