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:

82552810
97231738
1996641
8593471

Subtract row minima

We subtract the row minimum from each row:

7245180(-10)
806021(-17)
1005732(-9)
8492460(-1)

Subtract column minima

We subtract the column minimum from each column:

6245180
706021
005732
7492460
(-10)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

6245180
706021  x
005732  x
7492460
x

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 18. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

442700
706039
005750
5674280

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

442700
706039
005750  x
5674280
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 6. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

382100
640039
006356
5068280

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

382100  x
640039  x
006356  x
5068280  x

The optimal assignment

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

382100
640039
006356
5068280

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

82552810
97231738
1996641
8593471

The optimal value equals 71.