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:

62	77	96	64
42	82	69	30
75	47	11	31
44	9	93	26

Subtract row minima

We subtract the row minimum from each row:

0	15	34	2	(-62)
12	52	39	0	(-30)
64	36	0	20	(-11)
35	0	84	17	(-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:

0	15	34	2	x
12	52	39	0	x
64	36	0	20	x
35	0	84	17	x

The optimal assignment

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

0	15	34	2
12	52	39	0
64	36	0	20
35	0	84	17

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

62	77	96	64
42	82	69	30
75	47	11	31
44	9	93	26

The optimal value equals 112.