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:

7089669
8165975
76816383
41209972

Subtract row minima

We subtract the row minimum from each row:

6208861(-8)
085167(-8)
1318020(-63)
2107952(-20)

Subtract column minima

We subtract the column minimum from each column:

6208841
085147
131800
2107932
(-20)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

6208841
085147  x
131800  x
2107932
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 21. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

4106720
0295147
133900
005811

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

4106720
0295147
133900  x
005811
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 11. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

410569
0294036
245000
00470

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

410569  x
0294036  x
245000  x
00470  x

The optimal assignment

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

410569
0294036
245000
00470

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

7089669
8165975
76816383
41209972

The optimal value equals 151.