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:

4839461
7132669
9489023
64922417

Subtract row minima

We subtract the row minimum from each row:

4509158(-3)
6526063(-6)
0398114(-9)
477570(-17)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

4509158  x
6526063  x
0398114  x
477570  x

The optimal assignment

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

4509158
6526063
0398114
477570

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

4839461
7132669
9489023
64922417

The optimal value equals 35.