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:

3838683
1984454
7367289
2472213

Subtract row minima

We subtract the row minimum from each row:

3232077(-6)
1580050(-4)
6458190(-9)
0452011(-2)

Subtract column minima

We subtract the column minimum from each column:

320077
1548050
6426190
0132011
(-32)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

320077  x
1548050  x
6426190  x
0132011  x

The optimal assignment

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

320077
1548050
6426190
0132011

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

3838683
1984454
7367289
2472213

The optimal value equals 53.