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:

49	31	45	78
79	51	46	91
36	92	50	29
19	93	64	3

Subtract row minima

We subtract the row minimum from each row:

18	0	14	47	(-31)
33	5	0	45	(-46)
7	63	21	0	(-29)
16	90	61	0	(-3)

Subtract column minima

We subtract the column minimum from each column:

11	0	14	47
26	5	0	45
0	63	21	0
9	90	61	0
(-7)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

11	0	14	47	x
26	5	0	45	x
0	63	21	0	x
9	90	61	0	x

The optimal assignment

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

11	0	14	47
26	5	0	45
0	63	21	0
9	90	61	0

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

49	31	45	78
79	51	46	91
36	92	50	29
19	93	64	3

The optimal value equals 116.