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:

73	7	43	93
7	7	57	40
37	50	27	67
50	9	77	28

Subtract row minima

We subtract the row minimum from each row:

66	0	36	86	(-7)
0	0	50	33	(-7)
10	23	0	40	(-27)
41	0	68	19	(-9)

Subtract column minima

We subtract the column minimum from each column:

66	0	36	67
0	0	50	14
10	23	0	21
41	0	68	0
			(-19)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

66	0	36	67	x
0	0	50	14	x
10	23	0	21	x
41	0	68	0	x

The optimal assignment

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

66	0	36	67
0	0	50	14
10	23	0	21
41	0	68	0

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

73	7	43	93
7	7	57	40
37	50	27	67
50	9	77	28

The optimal value equals 69.