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:

22	58	6	85	39
30	85	82	4	19
6	22	49	5	55
87	21	58	7	97
51	5	78	93	45

Subtract row minima

We subtract the row minimum from each row:

16	52	0	79	33	(-6)
26	81	78	0	15	(-4)
1	17	44	0	50	(-5)
80	14	51	0	90	(-7)
46	0	73	88	40	(-5)

Subtract column minima

We subtract the column minimum from each column:

15	52	0	79	18
25	81	78	0	0
0	17	44	0	35
79	14	51	0	75
45	0	73	88	25
(-1)				(-15)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

15	52	0	79	18	x
25	81	78	0	0	x
0	17	44	0	35	x
79	14	51	0	75	x
45	0	73	88	25	x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

15	52	0	79	18
25	81	78	0	0
0	17	44	0	35
79	14	51	0	75
45	0	73	88	25

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

22	58	6	85	39
30	85	82	4	19
6	22	49	5	55
87	21	58	7	97
51	5	78	93	45

The optimal value equals 43.