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:

9425234
5510376
124552
73161643

Subtract row minima

We subtract the row minimum from each row:

9223032(-2)
494310(-6)
80148(-4)
570027(-16)

Subtract column minima

We subtract the column minimum from each column:

8423032
414310
00148
490027
(-8)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

8423032  x
414310  x
00148  x
490027  x

The optimal assignment

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

8423032
414310
00148
490027

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

9425234
5510376
124552
73161643

The optimal value equals 36.