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:

56	6	84	46
69	6	22	22
52	8	16	61
32	67	60	82

Subtract row minima

We subtract the row minimum from each row:

50	0	78	40	(-6)
63	0	16	16	(-6)
44	0	8	53	(-8)
0	35	28	50	(-32)

Subtract column minima

We subtract the column minimum from each column:

50	0	70	24
63	0	8	0
44	0	0	37
0	35	20	34
		(-8)	(-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

50	0	70	24	x
63	0	8	0	x
44	0	0	37	x
0	35	20	34	x

The optimal assignment

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

50	0	70	24
63	0	8	0
44	0	0	37
0	35	20	34

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

56	6	84	46
69	6	22	22
52	8	16	61
32	67	60	82

The optimal value equals 76.