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:

96	14	93	56
91	59	95	38
35	98	68	15
78	46	1	28

Subtract row minima

We subtract the row minimum from each row:

82	0	79	42	(-14)
53	21	57	0	(-38)
20	83	53	0	(-15)
77	45	0	27	(-1)

Subtract column minima

We subtract the column minimum from each column:

62	0	79	42
33	21	57	0
0	83	53	0
57	45	0	27
(-20)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

62	0	79	42	x
33	21	57	0	x
0	83	53	0	x
57	45	0	27	x

The optimal assignment

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

62	0	79	42
33	21	57	0
0	83	53	0
57	45	0	27

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

96	14	93	56
91	59	95	38
35	98	68	15
78	46	1	28

The optimal value equals 88.