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:

84	70	46
83	59	17
90	23	17

Subtract row minima

We subtract the row minimum from each row:

38	24	(-46)
66	42	(-17)
73	6	(-17)

Subtract column minima

We subtract the column minimum from each column:

0	18	0
28	36	0
35	0	0
(-38)	(-6)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

0	18	x
28	36	x
35	0	x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

0	18	0
28	36	0
35	0	0

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

84	70	46
83	59	17
90	23	17

The optimal value equals 124.