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:

47	42	60	26
50	78	63	17
71	50	15	84
37	47	59	31

Subtract row minima

We subtract the row minimum from each row:

21	16	34	0	(-26)
33	61	46	0	(-17)
56	35	0	69	(-15)
6	16	28	0	(-31)

Subtract column minima

We subtract the column minimum from each column:

15	0	34	0
27	45	46	0
50	19	0	69
0	0	28	0
(-6)	(-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

15	0	34	0	x
27	45	46	0	x
50	19	0	69	x
0	0	28	0	x

The optimal assignment

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

15	0	34	0
27	45	46	0
50	19	0	69
0	0	28	0

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

47	42	60	26
50	78	63	17
71	50	15	84
37	47	59	31

The optimal value equals 111.