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:

1461942
79781963
152562
1832586

Subtract row minima

We subtract the row minimum from each row:

1259920(-2)
6059044(-19)
051461(-1)
1226520(-6)

Subtract column minima

We subtract the column minimum from each column:

1233920
6033044
025461
120520
(-26)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

1233920  x
6033044  x
025461  x
120520  x

The optimal assignment

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

1233920
6033044
025461
120520

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

1461942
79781963
152562
1832586

The optimal value equals 54.