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:

23	80	7	56
52	26	12	93
13	93	20	74
86	95	40	72

Subtract row minima

We subtract the row minimum from each row:

16	73	0	49	(-7)
40	14	0	81	(-12)
0	80	7	61	(-13)
46	55	0	32	(-40)

Subtract column minima

We subtract the column minimum from each column:

16	59	0	17
40	0	0	49
0	66	7	29
46	41	0	0
	(-14)		(-32)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

16	59	0	17	x
40	0	0	49	x
0	66	7	29	x
46	41	0	0	x

The optimal assignment

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

16	59	0	17
40	0	0	49
0	66	7	29
46	41	0	0

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

23	80	7	56
52	26	12	93
13	93	20	74
86	95	40	72

The optimal value equals 118.