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	85	99	63
96	61	65	98
15	15	15	92
91	60	16	91

Subtract row minima

We subtract the row minimum from each row:

0	63	77	41	(-22)
35	0	4	37	(-61)
0	0	0	77	(-15)
75	44	0	75	(-16)

Subtract column minima

We subtract the column minimum from each column:

0	63	77	4
35	0	4	0
0	0	0	40
75	44	0	38
			(-37)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	63	77	4	x
35	0	4	0	x
0	0	0	40	x
75	44	0	38	x

The optimal assignment

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

0	63	77	4
35	0	4	0
0	0	0	40
75	44	0	38

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

22	85	99	63
96	61	65	98
15	15	15	92
91	60	16	91

The optimal value equals 151.