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:

1233626
378872
27594190
88186865

Subtract row minima

We subtract the row minimum from each row:

627020(-6)
048569(-3)
0321463(-27)
7005047(-18)

Subtract column minima

We subtract the column minimum from each column:

62700
048549
0321443
7005027
(-20)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

62700  x
048549
0321443
7005027  x
x

Create additional zeros

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

102700
008145
0281039
7405027

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

102700  x
008145
0281039
7405027
xx

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:

203700
007135
028029
7404017

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

203700  x
007135  x
028029  x
7404017  x

The optimal assignment

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

203700
007135
028029
7404017

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

1233626
378872
27594190
88186865

The optimal value equals 88.