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:

26374119
564411
41384342
3161556

Subtract row minima

We subtract the row minimum from each row:

718220(-19)
52007(-4)
3054(-38)
250950(-6)

Subtract column minima

We subtract the column minimum from each column:

418220
49007
0054
220950
(-3)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

418220  x
49007  x
0054  x
220950  x

The optimal assignment

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

418220
49007
0054
220950

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

26374119
564411
41384342
3161556

The optimal value equals 70.