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:

2470551963
7417466817
536254397
57948555
2416319578

Subtract row minima

We subtract the row minimum from each row:

55136044(-19)
57029510(-17)
465547320(-7)
52898000(-5)
80157962(-16)

Subtract column minima

We subtract the column minimum from each column:

05121044
52014510
415532320
47896500
3007962
(-5)(-15)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

05121044  x
52014510  x
415532320  x
47896500  x
3007962  x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

05121044
52014510
415532320
47896500
3007962

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

2470551963
7417466817
536254397
57948555
2416319578

The optimal value equals 84.