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:

14	43	60	97
76	52	3	36
15	15	66	11
58	13	94	9

Subtract row minima

We subtract the row minimum from each row:

0	29	46	83	(-14)
73	49	0	33	(-3)
4	4	55	0	(-11)
49	4	85	0	(-9)

Subtract column minima

We subtract the column minimum from each column:

0	25	46	83
73	45	0	33
4	0	55	0
49	0	85	0
	(-4)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	25	46	83	x
73	45	0	33	x
4	0	55	0	x
49	0	85	0	x

The optimal assignment

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

0	25	46	83
73	45	0	33
4	0	55	0
49	0	85	0

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

14	43	60	97
76	52	3	36
15	15	66	11
58	13	94	9

The optimal value equals 41.