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:

35	19	30	67
53	23	61	21
2	49	6	47
5	80	61	88

Subtract row minima

We subtract the row minimum from each row:

16	0	11	48	(-19)
32	2	40	0	(-21)
0	47	4	45	(-2)
0	75	56	83	(-5)

Subtract column minima

We subtract the column minimum from each column:

16	0	7	48
32	2	36	0
0	47	0	45
0	75	52	83
		(-4)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

16	0	7	48	x
32	2	36	0	x
0	47	0	45	x
0	75	52	83	x

The optimal assignment

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

16	0	7	48
32	2	36	0
0	47	0	45
0	75	52	83

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

35	19	30	67
53	23	61	21
2	49	6	47
5	80	61	88

The optimal value equals 51.