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:

5	42	59	25
54	85	41	99
14	75	40	41
56	21	19	84

Subtract row minima

We subtract the row minimum from each row:

0	37	54	20	(-5)
13	44	0	58	(-41)
0	61	26	27	(-14)
37	2	0	65	(-19)

Subtract column minima

We subtract the column minimum from each column:

0	35	54	0
13	42	0	38
0	59	26	7
37	0	0	45
	(-2)		(-20)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	35	54	0	x
13	42	0	38	x
0	59	26	7	x
37	0	0	45	x

The optimal assignment

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

0	35	54	0
13	42	0	38
0	59	26	7
37	0	0	45

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

5	42	59	25
54	85	41	99
14	75	40	41
56	21	19	84

The optimal value equals 101.