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:

87	32	48
24	46	2
5	64	17

Subtract row minima

We subtract the row minimum from each row:

55	0	16	(-32)
22	44	0	(-2)
0	59	12	(-5)

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 3 lines required to cover all zeros:

55	0	16	x
22	44	0	x
0	59	12	x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

55	0	16
22	44	0
0	59	12

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

87	32	48
24	46	2
5	64	17

The optimal value equals 39.