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:

12	29	25	25
88	22	60	23
86	10	23	17
82	20	98	64

Subtract row minima

We subtract the row minimum from each row:

0	17	13	13	(-12)
66	0	38	1	(-22)
76	0	13	7	(-10)
62	0	78	44	(-20)

Subtract column minima

We subtract the column minimum from each column:

0	17	0	12
66	0	25	0
76	0	0	6
62	0	65	43
		(-13)	(-1)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	17	0	12	x
66	0	25	0	x
76	0	0	6	x
62	0	65	43	x

The optimal assignment

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

0	17	0	12
66	0	25	0
76	0	0	6
62	0	65	43

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

12	29	25	25
88	22	60	23
86	10	23	17
82	20	98	64

The optimal value equals 78.