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

Solution

This is the cost matrix.

17	1	10	64
56	71	81	4
36	34	2	61
82	10	90	13

Subtract row minima

For each row, the minimum element is subtracted from all elements in that row.

16	0	9	63	(-1)
52	67	77	0	(-4)
34	32	0	59	(-2)
72	0	80	3	(-10)

Subtract column minima

For each column, the minimum element is subtracted from all elements in that column.

0	0	9	63
36	67	77	0
18	32	0	59
56	0	80	3
(-16)

Cover all zeros with a minimum number of lines

A total of 4 lines are required to cover all zeros.

0	0	9	63	x
36	67	77	0	x
18	32	0	59	x
56	0	80	3	x

The optimal assignment

Because there are 4 lines required, an optimal assignment exists among the zeros.

0	0	9	63
36	67	77	0
18	32	0	59
56	0	80	3

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

17	1	10	64
56	71	81	4
36	34	2	61
82	10	90	13

The total minimum cost is 33.