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:

7939622
48373919
22563838
75577193

Subtract row minima

We subtract the row minimum from each row:

7609319(-3)
2918200(-19)
0341616(-22)
1801436(-57)

Subtract column minima

We subtract the column minimum from each column:

7607919
291860
034216
180036
(-14)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

7607919  x
291860  x
034216  x
180036  x

The optimal assignment

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

7607919
291860
034216
180036

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

7939622
48373919
22563838
75577193

The optimal value equals 115.