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:

12425168
646632
2666529
1920927

Subtract row minima

We subtract the row minimum from each row:

0303956(-12)
624610(-2)
2005923(-6)
1011018(-9)

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:

0303956  x
624610  x
2005923  x
1011018  x

The optimal assignment

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

0303956
624610
2005923
1011018

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

12425168
646632
2666529
1920927

The optimal value equals 29.