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:

7546438
9045956
9259272
18256941

Subtract row minima

We subtract the row minimum from each row:

6738350(-8)
8439890(-6)
9057250(-2)
075123(-18)

Subtract column minima

We subtract the column minimum from each column:

6731100
8432640
905000
002623
(-7)(-25)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

6731100
8432640
905000  x
002623  x
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 10. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

572100
7422540
9050010
002633

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

572100
7422540
9050010
002633  x
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 21. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

36000
531540
6929010
004754

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

36000  x
531540  x
6929010  x
004754  x

The optimal assignment

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

36000
531540
6929010
004754

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

7546438
9045956
9259272
18256941

The optimal value equals 97.