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:

3611192
418527
94155393
94592473

Subtract row minima

We subtract the row minimum from each row:

3501091(-1)
014483(-4)
7903878(-15)
7035049(-24)

Subtract column minima

We subtract the column minimum from each column:

3501088
014480
7903875
7035046
(-3)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

3501088
014480  x
7903875
7035046  x
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 10. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

250078
024480
6902865
7045046

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

250078
024480  x
6902865
7045046
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 25. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

00053
049730
4402840
4545021

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

00053  x
049730  x
4402840  x
4545021  x

The optimal assignment

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

00053
049730
4402840
4545021

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

3611192
418527
94155393
94592473

The optimal value equals 82.