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:

62522018
19912497
45955928
79336321

Subtract row minima

We subtract the row minimum from each row:

443420(-18)
072578(-19)
1767310(-28)
5812420(-21)

Subtract column minima

We subtract the column minimum from each column:

442200
060378
1755290
580400
(-12)(-2)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

442200  x
060378  x
1755290  x
580400  x

The optimal assignment

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

442200
060378
1755290
580400

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

62522018
19912497
45955928
79336321

The optimal value equals 100.