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:

7288334
48596911
6887529
828731

Subtract row minima

We subtract the row minimum from each row:

6985031(-3)
3748580(-11)
5978430(-9)
751024(-7)

Subtract column minima

We subtract the column minimum from each column:

3284031
047580
2277430
380024
(-37)(-1)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

3284031  x
047580  x
2277430  x
380024  x

The optimal assignment

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

3284031
047580
2277430
380024

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

7288334
48596911
6887529
828731

The optimal value equals 68.