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:

9240785
62814943
9548852
5445968

Subtract row minima

We subtract the row minimum from each row:

8735730(-5)
193860(-43)
9108448(-4)
5005564(-4)

Subtract column minima

We subtract the column minimum from each column:

6835670
03800
7207848
3104964
(-19)(-6)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

6835670  x
03800  x
7207848
3104964
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 31. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

6866670
06900
4104717
001833

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

6866670  x
06900  x
4104717  x
001833  x

The optimal assignment

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

6866670
06900
4104717
001833

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

9240785
62814943
9548852
5445968

The optimal value equals 112.