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:

59977370
82829975
7961721
24918086

Subtract row minima

We subtract the row minimum from each row:

0381411(-59)
77240(-75)
0891014(-7)
0675662(-24)

Subtract column minima

We subtract the column minimum from each column:

031411
70140
082014
0604662
(-7)(-10)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

031411
70140  x
082014  x
0604662
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:

02707
110140
482014
0564258

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

02707
110140  x
482014
0564258
xx

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 7. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

02000
180210
47507
0494251

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

02000  x
180210  x
47507  x
0494251  x

The optimal assignment

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

02000
180210
47507
0494251

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

59977370
82829975
7961721
24918086

The optimal value equals 193.