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

Solution

This is the cost matrix.

99	35	3	23
66	80	11	85
56	30	72	86
72	30	51	93

Subtract row minima

For each row, the minimum element is subtracted from all elements in that row.

96	32	0	20	(-3)
55	69	0	74	(-11)
26	0	42	56	(-30)
42	0	21	63	(-30)

Subtract column minima

For each column, the minimum element is subtracted from all elements in that column.

70	32	0	0
29	69	0	54
0	0	42	36
16	0	21	43
(-26)			(-20)

Cover all zeros with a minimum number of lines

A total of 4 lines are required to cover all zeros.

70	32	0	0	x
29	69	0	54	x
0	0	42	36	x
16	0	21	43	x

The optimal assignment

Because there are 4 lines required, an optimal assignment exists among the zeros.

70	32	0	0
29	69	0	54
0	0	42	36
16	0	21	43

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

99	35	3	23
66	80	11	85
56	30	72	86
72	30	51	93

The total minimum cost is 120.