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:

62	69	95
26	73	65
98	11	79

Subtract row minima

We subtract the row minimum from each row:

0	7	33	(-62)
0	47	39	(-26)
87	0	68	(-11)

Subtract column minima

We subtract the column minimum from each column:

0	7	0
0	47	6
87	0	35
		(-33)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

0	7	0	x
0	47	6	x
87	0	35	x

The optimal assignment

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

0	7	0
0	47	6
87	0	35

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

62	69	95
26	73	65
98	11	79

The optimal value equals 132.