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:

42	98	80	29
81	22	97	5
38	70	70	51
31	52	49	47

Subtract row minima

We subtract the row minimum from each row:

13	69	51	0	(-29)
76	17	92	0	(-5)
0	32	32	13	(-38)
0	21	18	16	(-31)

Subtract column minima

We subtract the column minimum from each column:

13	52	33	0
76	0	74	0
0	15	14	13
0	4	0	16
	(-17)	(-18)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

13	52	33	0	x
76	0	74	0	x
0	15	14	13	x
0	4	0	16	x

The optimal assignment

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

13	52	33	0
76	0	74	0
0	15	14	13
0	4	0	16

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

42	98	80	29
81	22	97	5
38	70	70	51
31	52	49	47

The optimal value equals 138.