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:

68	61	91	10
86	90	70	78
76	94	52	87
77	33	77	76

Subtract row minima

We subtract the row minimum from each row:

58	51	81	0	(-10)
16	20	0	8	(-70)
24	42	0	35	(-52)
44	0	44	43	(-33)

Subtract column minima

We subtract the column minimum from each column:

42	51	81	0
0	20	0	8
8	42	0	35
28	0	44	43
(-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

42	51	81	0	x
0	20	0	8	x
8	42	0	35	x
28	0	44	43	x

The optimal assignment

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

42	51	81	0
0	20	0	8
8	42	0	35
28	0	44	43

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

68	61	91	10
86	90	70	78
76	94	52	87
77	33	77	76

The optimal value equals 181.