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:

22	79	22	16
21	21	47	52
11	18	74	47
62	72	9	52

Subtract row minima

We subtract the row minimum from each row:

6	63	6	0	(-16)
0	0	26	31	(-21)
0	7	63	36	(-11)
53	63	0	43	(-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:

6	63	6	0	x
0	0	26	31	x
0	7	63	36	x
53	63	0	43	x

The optimal assignment

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

6	63	6	0
0	0	26	31
0	7	63	36
53	63	0	43

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

22	79	22	16
21	21	47	52
11	18	74	47
62	72	9	52

The optimal value equals 57.