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.

83	1	14	11
12	14	10	34
76	93	45	32
65	86	16	92

Subtract row minima

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

82	0	13	10	(-1)
2	4	0	24	(-10)
44	61	13	0	(-32)
49	70	0	76	(-16)

Subtract column minima

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

80	0	13	10
0	4	0	24
42	61	13	0
47	70	0	76
(-2)

Cover all zeros with a minimum number of lines

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

80	0	13	10	x
0	4	0	24	x
42	61	13	0	x
47	70	0	76	x

The optimal assignment

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

80	0	13	10
0	4	0	24
42	61	13	0
47	70	0	76

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

83	1	14	11
12	14	10	34
76	93	45	32
65	86	16	92

The total minimum cost is 61.