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:

32	29	33	17
2	81	68	51
9	46	9	36
32	29	61	72

Subtract row minima

We subtract the row minimum from each row:

15	12	16	0	(-17)
0	79	66	49	(-2)
0	37	0	27	(-9)
3	0	32	43	(-29)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

15	12	16	0	x
0	79	66	49	x
0	37	0	27	x
3	0	32	43	x

The optimal assignment

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

15	12	16	0
0	79	66	49
0	37	0	27
3	0	32	43

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

32	29	33	17
2	81	68	51
9	46	9	36
32	29	61	72

The optimal value equals 57.