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:

75	29	63
43	49	44
9	46	88

Subtract row minima

We subtract the row minimum from each row:

46	0	34	(-29)
0	6	1	(-43)
0	37	79	(-9)

Subtract column minima

We subtract the column minimum from each column:

46	0	33
0	6	0
0	37	78
		(-1)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

46	0	33	x
0	6	0	x
0	37	78	x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

46	0	33
0	6	0
0	37	78

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

75	29	63
43	49	44
9	46	88

The optimal value equals 82.