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	26	51	9
93	39	15	58
83	59	73	65
76	21	44	70

Subtract row minima

We subtract the row minimum from each row:

88	17	42	0	(-9)
78	24	0	43	(-15)
24	0	14	6	(-59)
55	0	23	49	(-21)

Subtract column minima

We subtract the column minimum from each column:

64	17	42	0
54	24	0	43
0	0	14	6
31	0	23	49
(-24)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

64	17	42	0	x
54	24	0	43	x
0	0	14	6	x
31	0	23	49	x

The optimal assignment

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

64	17	42	0
54	24	0	43
0	0	14	6
31	0	23	49

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

97	26	51	9
93	39	15	58
83	59	73	65
76	21	44	70

The optimal value equals 128.