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.

72	20	22	4
89	18	4	11
16	14	10	32
10	71	18	30

Subtract row minima

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

68	16	18	0	(-4)
85	14	0	7	(-4)
6	4	0	22	(-10)
0	61	8	20	(-10)

Subtract column minima

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

68	12	18	0
85	10	0	7
6	0	0	22
0	57	8	20
	(-4)

Cover all zeros with a minimum number of lines

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

68	12	18	0	x
85	10	0	7	x
6	0	0	22	x
0	57	8	20	x

The optimal assignment

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

68	12	18	0
85	10	0	7
6	0	0	22
0	57	8	20

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

72	20	22	4
89	18	4	11
16	14	10	32
10	71	18	30

The total minimum cost is 32.