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:

85	80	71
4	61	52
23	95	2

Subtract row minima

We subtract the row minimum from each row:

14	9	0	(-71)
0	57	48	(-4)
21	93	0	(-2)

Subtract column minima

We subtract the column minimum from each column:

14	0	0
0	48	48
21	84	0
	(-9)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

14	0	0	x
0	48	48	x
21	84	0	x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

14	0	0
0	48	48
21	84	0

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

85	80	71
4	61	52
23	95	2

The optimal value equals 86.