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:

28	49	85	70
93	59	96	34
28	15	77	81
12	23	95	64

Negate all values

Because the objective is to maximize the total cost we negate all elements:

-28	-49	-85	-70
-93	-59	-96	-34
-28	-15	-77	-81
-12	-23	-95	-64

Make the matrix nonnegative

The cost matrix contains negative elements, we add 96 to each entry to make the cost matrix nonnegative:

68	47	11	26
3	37	0	62
68	81	19	15
84	73	1	32

Subtract row minima

We subtract the row minimum from each row:

57	36	0	15	(-11)
3	37	0	62
53	66	4	0	(-15)
83	72	0	31	(-1)

Subtract column minima

We subtract the column minimum from each column:

54	0	0	15
0	1	0	62
50	30	4	0
80	36	0	31
(-3)	(-36)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

54	0	0	15	x
0	1	0	62	x
50	30	4	0	x
80	36	0	31	x

The optimal assignment

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

54	0	0	15
0	1	0	62
50	30	4	0
80	36	0	31

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

28	49	85	70
93	59	96	34
28	15	77	81
12	23	95	64

The optimal value equals 318.