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:

55	76	57	35
6	89	72	10
32	45	16	33
65	95	21	27

Subtract row minima

We subtract the row minimum from each row:

20	41	22	0	(-35)
0	83	66	4	(-6)
16	29	0	17	(-16)
44	74	0	6	(-21)

Subtract column minima

We subtract the column minimum from each column:

20	12	22	0
0	54	66	4
16	0	0	17
44	45	0	6
	(-29)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

20	12	22	0	x
0	54	66	4	x
16	0	0	17	x
44	45	0	6	x

The optimal assignment

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

20	12	22	0
0	54	66	4
16	0	0	17
44	45	0	6

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

55	76	57	35
6	89	72	10
32	45	16	33
65	95	21	27

The optimal value equals 107.