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:

92188521
93439618
5773583
33957751

Subtract row minima

We subtract the row minimum from each row:

740673(-18)
7525780(-18)
5268078(-5)
0624418(-33)

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:

740673  x
7525780  x
5268078  x
0624418  x

The optimal assignment

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

740673
7525780
5268078
0624418

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

92188521
93439618
5773583
33957751

The optimal value equals 74.