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:

64	90	9	42
15	55	33	58
25	26	17	91
58	53	18	17

Subtract row minima

We subtract the row minimum from each row:

55	81	0	33	(-9)
0	40	18	43	(-15)
8	9	0	74	(-17)
41	36	1	0	(-17)

Subtract column minima

We subtract the column minimum from each column:

55	72	0	33
0	31	18	43
8	0	0	74
41	27	1	0
	(-9)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

55	72	0	33	x
0	31	18	43	x
8	0	0	74	x
41	27	1	0	x

The optimal assignment

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

55	72	0	33
0	31	18	43
8	0	0	74
41	27	1	0

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

64	90	9	42
15	55	33	58
25	26	17	91
58	53	18	17

The optimal value equals 67.