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:

19	83	38	95
81	55	92	91
28	93	2	87
26	3	40	25

Subtract row minima

We subtract the row minimum from each row:

0	64	19	76	(-19)
26	0	37	36	(-55)
26	91	0	85	(-2)
23	0	37	22	(-3)

Subtract column minima

We subtract the column minimum from each column:

0	64	19	54
26	0	37	14
26	91	0	63
23	0	37	0
			(-22)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	64	19	54	x
26	0	37	14	x
26	91	0	63	x
23	0	37	0	x

The optimal assignment

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

0	64	19	54
26	0	37	14
26	91	0	63
23	0	37	0

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

19	83	38	95
81	55	92	91
28	93	2	87
26	3	40	25

The optimal value equals 101.