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:

63	54	57	91
88	61	68	73
54	27	30	76
22	71	53	69

Subtract row minima

We subtract the row minimum from each row:

9	0	3	37	(-54)
27	0	7	12	(-61)
27	0	3	49	(-27)
0	49	31	47	(-22)

Subtract column minima

We subtract the column minimum from each column:

9	0	0	25
27	0	4	0
27	0	0	37
0	49	28	35
		(-3)	(-12)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

9	0	0	25	x
27	0	4	0	x
27	0	0	37	x
0	49	28	35	x

The optimal assignment

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

9	0	0	25
27	0	4	0
27	0	0	37
0	49	28	35

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

63	54	57	91
88	61	68	73
54	27	30	76
22	71	53	69

The optimal value equals 179.