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:

458887
861855
546044

Subtract row minima

We subtract the row minimum from each row:

04342(-45)
68037(-18)
10160(-44)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

04342  x
68037  x
10160  x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

04342
68037
10160

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

458887
861855
546044

The optimal value equals 107.