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:

80	60	9
45	31	44
78	28	75

Subtract row minima

We subtract the row minimum from each row:

71	51	0	(-9)
14	0	13	(-31)
50	0	47	(-28)

Subtract column minima

We subtract the column minimum from each column:

57	51	0
0	0	13
36	0	47
(-14)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

57	51	0	x
0	0	13	x
36	0	47	x

The optimal assignment

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

57	51	0
0	0	13
36	0	47

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

80	60	9
45	31	44
78	28	75

The optimal value equals 82.