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:

12	42	51	68
64	6	63	2
26	6	65	29
19	20	9	27

Subtract row minima

We subtract the row minimum from each row:

0	30	39	56	(-12)
62	4	61	0	(-2)
20	0	59	23	(-6)
10	11	0	18	(-9)

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:

0	30	39	56	x
62	4	61	0	x
20	0	59	23	x
10	11	0	18	x

The optimal assignment

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

0	30	39	56
62	4	61	0
20	0	59	23
10	11	0	18

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

12	42	51	68
64	6	63	2
26	6	65	29
19	20	9	27

The optimal value equals 29.