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:

17	58	46	25	44
27	70	99	52	45
5	34	15	63	15
63	93	72	25	13
74	16	93	82	83

Subtract row minima

We subtract the row minimum from each row:

0	41	29	8	27	(-17)
0	43	72	25	18	(-27)
0	29	10	58	10	(-5)
50	80	59	12	0	(-13)
58	0	77	66	67	(-16)

Subtract column minima

We subtract the column minimum from each column:

0	41	19	0	27
0	43	62	17	18
0	29	0	50	10
50	80	49	4	0
58	0	67	58	67
		(-10)	(-8)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

0	41	19	0	27	x
0	43	62	17	18	x
0	29	0	50	10	x
50	80	49	4	0	x
58	0	67	58	67	x

The optimal assignment

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

0	41	19	0	27
0	43	62	17	18
0	29	0	50	10
50	80	49	4	0
58	0	67	58	67

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

17	58	46	25	44
27	70	99	52	45
5	34	15	63	15
63	93	72	25	13
74	16	93	82	83

The optimal value equals 96.