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.

3	68	20	5
36	42	27	41
23	86	27	14
66	96	21	43

Subtract row minima

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

0	65	17	2	(-3)
9	15	0	14	(-27)
9	72	13	0	(-14)
45	75	0	22	(-21)

Subtract column minima

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

0	50	17	2
9	0	0	14
9	57	13	0
45	60	0	22
	(-15)

Cover all zeros with a minimum number of lines

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

0	50	17	2	x
9	0	0	14	x
9	57	13	0	x
45	60	0	22	x

The optimal assignment

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

0	50	17	2
9	0	0	14
9	57	13	0
45	60	0	22

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

3	68	20	5
36	42	27	41
23	86	27	14
66	96	21	43

The total minimum cost is 80.