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:

99	91	58	21
67	24	15	67
51	90	2	41
35	74	93	76

Subtract row minima

We subtract the row minimum from each row:

78	70	37	0	(-21)
52	9	0	52	(-15)
49	88	0	39	(-2)
0	39	58	41	(-35)

Subtract column minima

We subtract the column minimum from each column:

78	61	37	0
52	0	0	52
49	79	0	39
0	30	58	41
	(-9)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

78	61	37	0	x
52	0	0	52	x
49	79	0	39	x
0	30	58	41	x

The optimal assignment

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

78	61	37	0
52	0	0	52
49	79	0	39
0	30	58	41

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

99	91	58	21
67	24	15	67
51	90	2	41
35	74	93	76

The optimal value equals 82.