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:

47	66	1	10
87	59	46	47
84	80	54	97
62	13	14	18

Subtract row minima

We subtract the row minimum from each row:

46	65	0	9	(-1)
41	13	0	1	(-46)
30	26	0	43	(-54)
49	0	1	5	(-13)

Subtract column minima

We subtract the column minimum from each column:

16	65	0	8
11	13	0	0
0	26	0	42
19	0	1	4
(-30)			(-1)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

16	65	0	8	x
11	13	0	0	x
0	26	0	42	x
19	0	1	4	x

The optimal assignment

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

16	65	0	8
11	13	0	0
0	26	0	42
19	0	1	4

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

47	66	1	10
87	59	46	47
84	80	54	97
62	13	14	18

The optimal value equals 145.