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:

95	59	59	93
82	95	55	17
17	85	21	74
99	46	9	29

Subtract row minima

We subtract the row minimum from each row:

36	0	0	34	(-59)
65	78	38	0	(-17)
0	68	4	57	(-17)
90	37	0	20	(-9)

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:

36	0	0	34	x
65	78	38	0	x
0	68	4	57	x
90	37	0	20	x

The optimal assignment

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

36	0	0	34
65	78	38	0
0	68	4	57
90	37	0	20

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

95	59	59	93
82	95	55	17
17	85	21	74
99	46	9	29

The optimal value equals 102.