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:

39	88	26	99
8	93	17	70
19	63	86	8
69	23	65	26

Subtract row minima

We subtract the row minimum from each row:

13	62	0	73	(-26)
0	85	9	62	(-8)
11	55	78	0	(-8)
46	0	42	3	(-23)

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 4 lines required to cover all zeros:

13	62	0	73	x
0	85	9	62	x
11	55	78	0	x
46	0	42	3	x

The optimal assignment

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

13	62	0	73
0	85	9	62
11	55	78	0
46	0	42	3

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

39	88	26	99
8	93	17	70
19	63	86	8
69	23	65	26

The optimal value equals 65.