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:

26	30	82	76
56	16	33	86
81	26	47	18
39	52	35	58

Subtract row minima

We subtract the row minimum from each row:

0	4	56	50	(-26)
40	0	17	70	(-16)
63	8	29	0	(-18)
4	17	0	23	(-35)

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	4	56	50	x
40	0	17	70	x
63	8	29	0	x
4	17	0	23	x

The optimal assignment

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

0	4	56	50
40	0	17	70
63	8	29	0
4	17	0	23

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

26	30	82	76
56	16	33	86
81	26	47	18
39	52	35	58

The optimal value equals 95.