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:

5425925
54854199
14754041
56211984

Subtract row minima

We subtract the row minimum from each row:

0375420(-5)
1344058(-41)
0612627(-14)
372065(-19)

Subtract column minima

We subtract the column minimum from each column:

035540
1342038
059267
370045
(-2)(-20)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

035540  x
1342038  x
059267  x
370045  x

The optimal assignment

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

035540
1342038
059267
370045

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

5425925
54854199
14754041
56211984

The optimal value equals 101.