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:

84	13	65	1
71	2	6	39
67	35	31	80
30	81	45	52

Subtract row minima

We subtract the row minimum from each row:

83	12	64	0	(-1)
69	0	4	37	(-2)
36	4	0	49	(-31)
0	51	15	22	(-30)

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:

83	12	64	0	x
69	0	4	37	x
36	4	0	49	x
0	51	15	22	x

The optimal assignment

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

83	12	64	0
69	0	4	37
36	4	0	49
0	51	15	22

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

84	13	65	1
71	2	6	39
67	35	31	80
30	81	45	52

The optimal value equals 64.