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:

63545791
88616873
54273076
22715369

Subtract row minima

We subtract the row minimum from each row:

90337(-54)
270712(-61)
270349(-27)
0493147(-22)

Subtract column minima

We subtract the column minimum from each column:

90025
27040
270037
0492835
(-3)(-12)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

90025  x
27040  x
270037  x
0492835  x

The optimal assignment

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

90025
27040
270037
0492835

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

63545791
88616873
54273076
22715369

The optimal value equals 179.