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:

93	85	67	85
57	85	44	75
48	69	81	77
5	21	57	26

Subtract row minima

We subtract the row minimum from each row:

26	18	0	18	(-67)
13	41	0	31	(-44)
0	21	33	29	(-48)
0	16	52	21	(-5)

Subtract column minima

We subtract the column minimum from each column:

26	2	0	0
13	25	0	13
0	5	33	11
0	0	52	3
	(-16)		(-18)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

26	2	0	0	x
13	25	0	13	x
0	5	33	11	x
0	0	52	3	x

The optimal assignment

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

26	2	0	0
13	25	0	13
0	5	33	11
0	0	52	3

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

93	85	67	85
57	85	44	75
48	69	81	77
5	21	57	26

The optimal value equals 198.