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:

27	42	46	78
94	4	1	99
75	79	38	3
34	27	3	59

Subtract row minima

We subtract the row minimum from each row:

0	15	19	51	(-27)
93	3	0	98	(-1)
72	76	35	0	(-3)
31	24	0	56	(-3)

Subtract column minima

We subtract the column minimum from each column:

0	12	19	51
93	0	0	98
72	73	35	0
31	21	0	56
	(-3)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	12	19	51	x
93	0	0	98	x
72	73	35	0	x
31	21	0	56	x

The optimal assignment

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

0	12	19	51
93	0	0	98
72	73	35	0
31	21	0	56

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

27	42	46	78
94	4	1	99
75	79	38	3
34	27	3	59

The optimal value equals 37.