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:

49	65	50	78
40	31	60	79
77	35	74	33
88	52	29	56

Subtract row minima

We subtract the row minimum from each row:

0	16	1	29	(-49)
9	0	29	48	(-31)
44	2	41	0	(-33)
59	23	0	27	(-29)

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:

0	16	1	29	x
9	0	29	48	x
44	2	41	0	x
59	23	0	27	x

The optimal assignment

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

0	16	1	29
9	0	29	48
44	2	41	0
59	23	0	27

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

49	65	50	78
40	31	60	79
77	35	74	33
88	52	29	56

The optimal value equals 142.