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:

23	24	96	5
98	23	39	9
93	61	14	37
93	7	85	78

Subtract row minima

We subtract the row minimum from each row:

18	19	91	0	(-5)
89	14	30	0	(-9)
79	47	0	23	(-14)
86	0	78	71	(-7)

Subtract column minima

We subtract the column minimum from each column:

0	19	91	0
71	14	30	0
61	47	0	23
68	0	78	71
(-18)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	19	91	0	x
71	14	30	0	x
61	47	0	23	x
68	0	78	71	x

The optimal assignment

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

0	19	91	0
71	14	30	0
61	47	0	23
68	0	78	71

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

23	24	96	5
98	23	39	9
93	61	14	37
93	7	85	78

The optimal value equals 53.