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:

899080776
643017686
321641681
4591944974
2257582461

Subtract row minima

We subtract the row minimum from each row:

838474710(-6)
582411080(-6)
311540670(-1)
04649429(-45)
03536239(-22)

Subtract column minima

We subtract the column minimum from each column:

836963710
5890080
31029670
03138429
02025239
(-15)(-11)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

836963710  x
5890080  x
31029670  x
03138429
02025239
x

Create additional zeros

The number of lines is smaller than 5. The smallest uncovered number is 2. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

856963710
6090080
33029670
02936227
01823037

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

856963710  x
6090080  x
33029670  x
02936227  x
01823037  x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

856963710
6090080
33029670
02936227
01823037

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

899080776
643017686
321641681
4591944974
2257582461

The optimal value equals 108.