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:

91149913
52936040
76319096
855928

Subtract row minima

We subtract the row minimum from each row:

781860(-13)
1253200(-40)
4505965(-31)
800873(-5)

Subtract column minima

We subtract the column minimum from each column:

661660
05300
3303965
680673
(-12)(-20)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

661660  x
05300  x
3303965
680673
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 3. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

664660
05600
3003662
650640

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

664660
05600  x
3003662
650640
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 30. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

364360
086030
00662
350340

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

364360  x
086030  x
00662  x
350340  x

The optimal assignment

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

364360
086030
00662
350340

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

91149913
52936040
76319096
855928

The optimal value equals 154.