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:

8	34	24	83
75	63	50	77
57	34	93	15
67	8	82	79

Subtract row minima

We subtract the row minimum from each row:

0	26	16	75	(-8)
25	13	0	27	(-50)
42	19	78	0	(-15)
59	0	74	71	(-8)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	26	16	75	x
25	13	0	27	x
42	19	78	0	x
59	0	74	71	x

The optimal assignment

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

0	26	16	75
25	13	0	27
42	19	78	0
59	0	74	71

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

8	34	24	83
75	63	50	77
57	34	93	15
67	8	82	79

The optimal value equals 81.