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:

22	4	81	66
81	5	66	7
54	45	21	51
1	89	24	54

Subtract row minima

We subtract the row minimum from each row:

18	0	77	62	(-4)
76	0	61	2	(-5)
33	24	0	30	(-21)
0	88	23	53	(-1)

Subtract column minima

We subtract the column minimum from each column:

18	0	77	60
76	0	61	0
33	24	0	28
0	88	23	51
			(-2)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

18	0	77	60	x
76	0	61	0	x
33	24	0	28	x
0	88	23	51	x

The optimal assignment

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

18	0	77	60
76	0	61	0
33	24	0	28
0	88	23	51

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

22	4	81	66
81	5	66	7
54	45	21	51
1	89	24	54

The optimal value equals 33.