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:

5257470
76325290
48151725
25393882

Subtract row minima

We subtract the row minimum from each row:

4853066(-4)
4402058(-32)
330210(-15)
0141357(-25)

Subtract column minima

We subtract the column minimum from each column:

4853056
4402048
33020
0141347
(-10)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

4853056  x
4402048  x
33020  x
0141347  x

The optimal assignment

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

4853056
4402048
33020
0141347

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

5257470
76325290
48151725
25393882

The optimal value equals 86.