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:

40	58	92	11
44	9	23	86
5	18	86	67
67	75	45	76

Subtract row minima

We subtract the row minimum from each row:

29	47	81	0	(-11)
35	0	14	77	(-9)
0	13	81	62	(-5)
22	30	0	31	(-45)

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:

29	47	81	0	x
35	0	14	77	x
0	13	81	62	x
22	30	0	31	x

The optimal assignment

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

29	47	81	0
35	0	14	77
0	13	81	62
22	30	0	31

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

40	58	92	11
44	9	23	86
5	18	86	67
67	75	45	76

The optimal value equals 70.