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:

48	6	54	72
59	56	50	75
87	36	5	78
82	13	11	25

Subtract row minima

We subtract the row minimum from each row:

42	0	48	66	(-6)
9	6	0	25	(-50)
82	31	0	73	(-5)
71	2	0	14	(-11)

Subtract column minima

We subtract the column minimum from each column:

33	0	48	52
0	6	0	11
73	31	0	59
62	2	0	0
(-9)			(-14)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

33	0	48	52	x
0	6	0	11	x
73	31	0	59	x
62	2	0	0	x

The optimal assignment

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

33	0	48	52
0	6	0	11
73	31	0	59
62	2	0	0

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

48	6	54	72
59	56	50	75
87	36	5	78
82	13	11	25

The optimal value equals 95.