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:

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

Subtract row minima

We subtract the row minimum from each row:

71	46	79	27	4	0	(-12)
0	3	42	3	40	47	(-30)
11	11	5	0	4	2	(-1)
63	59	63	75	0	41	(-16)
50	76	0	23	10	67	(-8)
0	26	55	38	21	31	(-44)

Subtract column minima

We subtract the column minimum from each column:

71	43	79	27	4	0
0	0	42	3	40	47
11	8	5	0	4	2
63	56	63	75	0	41
50	73	0	23	10	67
0	23	55	38	21	31
	(-3)

Cover all zeros with a minimum number of lines

There are 6 lines required to cover all zeros:

71	43	79	27	4	0	x
0	0	42	3	40	47	x
11	8	5	0	4	2	x
63	56	63	75	0	41	x
50	73	0	23	10	67	x
0	23	55	38	21	31	x

The optimal assignment

Because there are 6 lines required, the zeros cover an optimal assignment:

71	43	79	27	4	0
0	0	42	3	40	47
11	8	5	0	4	2
63	56	63	75	0	41
50	73	0	23	10	67
0	23	55	38	21	31

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

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

The optimal value equals 114.

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

71	43	79	27	4	0	x
0	0	42	3	40	47	x
11	8	5	0	4	2	x
63	56	63	75	0	41	x
50	73	0	23	10	67	x
0	23	55	38	21	31	x

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

71	43	79	27	4	0	x
0	0	42	3	40	47	x
11	8	5	0	4	2	x
63	56	63	75	0	41	x
50	73	0	23	10	67	x
0	23	55	38	21	31	x

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75

71	43	79	27	4	0	x
0	0	42	3	40	47	x
11	8	5	0	4	2	x
63	56	63	75	0	41	x
50	73	0	23	10	67	x
0	23	55	38	21	31	x

83	58	91	39	16	12
30	33	72	33	70	77
12	12	6	1	5	3
79	75	79	91	16	57
58	84	8	31	18	75
44	70	99	82	65	75