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:

55196529
80844845
56448519
86879271

Subtract row minima

We subtract the row minimum from each row:

3604610(-19)
353930(-45)
3725660(-19)
1516210(-71)

Subtract column minima

We subtract the column minimum from each column:

2104310
203900
2225630
016180
(-15)(-3)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

2104310  x
203900  x
2225630  x
016180  x

The optimal assignment

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

2104310
203900
2225630
016180

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

55196529
80844845
56448519
86879271

The optimal value equals 172.