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:

43	12	62	31
9	87	68	3
91	82	67	92
17	46	80	9

Subtract row minima

We subtract the row minimum from each row:

31	0	50	19	(-12)
6	84	65	0	(-3)
24	15	0	25	(-67)
8	37	71	0	(-9)

Subtract column minima

We subtract the column minimum from each column:

25	0	50	19
0	84	65	0
18	15	0	25
2	37	71	0
(-6)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

25	0	50	19	x
0	84	65	0	x
18	15	0	25	x
2	37	71	0	x

The optimal assignment

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

25	0	50	19
0	84	65	0
18	15	0	25
2	37	71	0

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

43	12	62	31
9	87	68	3
91	82	67	92
17	46	80	9

The optimal value equals 97.