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:

26674356
5125416
65376793
88937176

Subtract row minima

We subtract the row minimum from each row:

0411730(-26)
4721012(-4)
2803056(-37)
172205(-71)

Subtract column minima

We subtract the column minimum from each column:

0411725
472107
2803051
172200
(-5)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0411725  x
472107  x
2803051  x
172200  x

The optimal assignment

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

0411725
472107
2803051
172200

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

26674356
5125416
65376793
88937176

The optimal value equals 143.