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:

88	93	60
22	14	62
27	26	79

Subtract row minima

We subtract the row minimum from each row:

28	33	0	(-60)
8	0	48	(-14)
1	0	53	(-26)

Subtract column minima

We subtract the column minimum from each column:

27	33	0
7	0	48
0	0	53
(-1)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

27	33	0	x
7	0	48	x
0	0	53	x

The optimal assignment

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

27	33	0
7	0	48
0	0	53

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

88	93	60
22	14	62
27	26	79

The optimal value equals 101.