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:

15884181
32421585
82904150
68457489

Subtract row minima

We subtract the row minimum from each row:

0732666(-15)
1727070(-15)
414909(-41)
2302944(-45)

Subtract column minima

We subtract the column minimum from each column:

0732657
1727061
414900
2302935
(-9)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0732657  x
1727061  x
414900  x
2302935  x

The optimal assignment

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

0732657
1727061
414900
2302935

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

15884181
32421585
82904150
68457489

The optimal value equals 125.