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:

82	71	93	31
55	92	72	17
31	29	99	76
5	82	61	81

Subtract row minima

We subtract the row minimum from each row:

51	40	62	0	(-31)
38	75	55	0	(-17)
2	0	70	47	(-29)
0	77	56	76	(-5)

Subtract column minima

We subtract the column minimum from each column:

51	40	7	0
38	75	0	0
2	0	15	47
0	77	1	76
		(-55)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

51	40	7	0	x
38	75	0	0	x
2	0	15	47	x
0	77	1	76	x

The optimal assignment

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

51	40	7	0
38	75	0	0
2	0	15	47
0	77	1	76

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

82	71	93	31
55	92	72	17
31	29	99	76
5	82	61	81

The optimal value equals 137.