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:

2437291097
7953628283
1930168291
3973671345
3281391899

Subtract row minima

We subtract the row minimum from each row:

142719087(-10)
26092930(-53)
31406675(-16)
266054032(-13)
146321081(-18)

Subtract column minima

We subtract the column minimum from each column:

112719057
2309290
01406645
23605402
116321051
(-3)(-30)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

112719057
2309290  x
01406645  x
23605402
116321051
x

Create additional zeros

The number of lines is smaller than 5. The smallest uncovered number is 2. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

92517055
2309310
01406845
21585200
96119049

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

92517055
2309310  x
01406845  x
21585200  x
96119049
x

Create additional zeros

The number of lines is smaller than 5. The smallest uncovered number is 9. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

0168046
2309400
01407745
21585290
05210040

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

0168046  x
2309400  x
01407745  x
21585290  x
05210040  x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

0168046
2309400
01407745
21585290
05210040

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

2437291097
7953628283
1930168291
3973671345
3281391899

The optimal value equals 156.