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:

19162338
43481616
60864414
72954319

Subtract row minima

We subtract the row minimum from each row:

30722(-16)
273200(-16)
4672300(-14)
5376240(-19)

Subtract column minima

We subtract the column minimum from each column:

00722
243200
4372300
5076240
(-3)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

00722  x
243200  x
4372300
5076240
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 24. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

00746
2432024
194860
265200

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

00746  x
2432024
194860
265200
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 19. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

002665
513024
02960
73300

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

002665  x
513024  x
02960  x
73300  x

The optimal assignment

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

002665
513024
02960
73300

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

19162338
43481616
60864414
72954319

The optimal value equals 111.