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:

1666213
32337658
3959416
35517833

Subtract row minima

We subtract the row minimum from each row:

1464011(-2)
014426(-32)
3555012(-4)
218450(-33)

Subtract column minima

We subtract the column minimum from each column:

1463011
004426
3554012
217450
(-1)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

1463011
004426  x
3554012
217450  x
x

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:

35200
005526
244301
217560

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

35200
005526  x
244301
217560
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 2. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

15000
005728
224101
015560

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

15000  x
005728  x
224101  x
015560  x

The optimal assignment

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

15000
005728
224101
015560

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

1666213
32337658
3959416
35517833

The optimal value equals 85.