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:

19985854
84818326
6154431
6380319

Subtract row minima

We subtract the row minimum from each row:

0793935(-19)
5855570(-26)
6053420(-1)
5471220(-9)

Subtract column minima

We subtract the column minimum from each column:

0261735
582350
600200
541800
(-53)(-22)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0261735  x
582350  x
600200  x
541800  x

The optimal assignment

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

0261735
582350
600200
541800

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

19985854
84818326
6154431
6380319

The optimal value equals 130.