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:

60239765
83363283
44612970
29259696

Subtract row minima

We subtract the row minimum from each row:

3707442(-23)
514051(-32)
1532041(-29)
407171(-25)

Subtract column minima

We subtract the column minimum from each column:

330741
474010
113200
007130
(-4)(-41)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

330741  x
474010  x
113200  x
007130  x

The optimal assignment

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

330741
474010
113200
007130

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

60239765
83363283
44612970
29259696

The optimal value equals 154.