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:

97	98	23	64
25	82	80	87
49	44	41	4
84	17	18	94

Subtract row minima

We subtract the row minimum from each row:

74	75	0	41	(-23)
0	57	55	62	(-25)
45	40	37	0	(-4)
67	0	1	77	(-17)

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:

74	75	0	41	x
0	57	55	62	x
45	40	37	0	x
67	0	1	77	x

The optimal assignment

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

74	75	0	41
0	57	55	62
45	40	37	0
67	0	1	77

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

97	98	23	64
25	82	80	87
49	44	41	4
84	17	18	94

The optimal value equals 69.