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

Solution

This is the cost matrix.

2	10	33	2
58	9	36	66
67	54	19	33
67	69	91	24

Subtract row minima

For each row, the minimum element is subtracted from all elements in that row.

0	8	31	0	(-2)
49	0	27	57	(-9)
48	35	0	14	(-19)
43	45	67	0	(-24)

Subtract column minima

Because each column already contains a zero, subtracting the column minima has no effect.

Cover all zeros with a minimum number of lines

A total of 4 lines are required to cover all zeros.

0	8	31	0	x
49	0	27	57	x
48	35	0	14	x
43	45	67	0	x

The optimal assignment

Because there are 4 lines required, an optimal assignment exists among the zeros.

0	8	31	0
49	0	27	57
48	35	0	14
43	45	67	0

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

2	10	33	2
58	9	36	66
67	54	19	33
67	69	91	24

The total minimum cost is 54.