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:

44	6	80	39	28
58	74	80	69	76
3	60	63	55	98
72	97	2	63	62
46	73	90	40	84

Subtract row minima

We subtract the row minimum from each row:

38	0	74	33	22	(-6)
0	16	22	11	18	(-58)
0	57	60	52	95	(-3)
70	95	0	61	60	(-2)
6	33	50	0	44	(-40)

Subtract column minima

We subtract the column minimum from each column:

38	0	74	33	4
0	16	22	11	0
0	57	60	52	77
70	95	0	61	42
6	33	50	0	26
				(-18)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

38	0	74	33	4	x
0	16	22	11	0	x
0	57	60	52	77	x
70	95	0	61	42	x
6	33	50	0	26	x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

38	0	74	33	4
0	16	22	11	0
0	57	60	52	77
70	95	0	61	42
6	33	50	0	26

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

44	6	80	39	28
58	74	80	69	76
3	60	63	55	98
72	97	2	63	62
46	73	90	40	84

The optimal value equals 127.