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:

76	87	13	30
66	48	16	42
43	8	1	37
85	33	49	64

Subtract row minima

We subtract the row minimum from each row:

63	74	0	17	(-13)
50	32	0	26	(-16)
42	7	0	36	(-1)
52	0	16	31	(-33)

Subtract column minima

We subtract the column minimum from each column:

21	74	0	0
8	32	0	9
0	7	0	19
10	0	16	14
(-42)			(-17)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

21	74	0	0	x
8	32	0	9	x
0	7	0	19	x
10	0	16	14	x

The optimal assignment

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

21	74	0	0
8	32	0	9
0	7	0	19
10	0	16	14

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

76	87	13	30
66	48	16	42
43	8	1	37
85	33	49	64

The optimal value equals 122.