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:

3083785028
4992745432
548613421
6153175098
2813715851

Subtract row minima

We subtract the row minimum from each row:

25550220(-28)
176042220(-32)
460532613(-8)
443603381(-17)
150584538(-13)

Subtract column minima

We subtract the column minimum from each column:

0555000
15604200
44053413
423601181
130582338
(-2)(-22)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0555000  x
15604200  x
44053413
423601181  x
130582338
x

Create additional zeros

The number of lines is smaller than 5. The smallest uncovered number is 4. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

0595000
15644200
4004909
424001181
90541934

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

0595000  x
15644200  x
4004909  x
424001181  x
90541934  x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

0595000
15644200
4004909
424001181
90541934

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

3083785028
4992745432
548613421
6153175098
2813715851

The optimal value equals 126.