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:

23802468
45874759
29333865
1516663

Subtract row minima

We subtract the row minimum from each row:

057145(-23)
042214(-45)
04936(-29)
1213630(-3)

Subtract column minima

We subtract the column minimum from each column:

053045
038114
00836
129620
(-4)(-1)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

053045  x
038114  x
00836  x
129620  x

The optimal assignment

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

053045
038114
00836
129620

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

23802468
45874759
29333865
1516663

The optimal value equals 105.