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:

5280809672426
9152564777456
69743852541122
8811489407240
889141790111
707294797391
953555882210

Subtract row minima

We subtract the row minimum from each row:

4573738901719(-7)
8602059726951(-5)
5863274143011(-11)
073681326432(-8)
879031689010(-1)
697193786380(-1)
93335368008(-2)

Subtract column minima

We subtract the column minimum from each column:

4573708301719
8601753726951
5863243543011
073375326432
879001089010
697190726380
93335008008
(-3)(-6)

Cover all zeros with a minimum number of lines

There are 7 lines required to cover all zeros:

4573708301719  x
8601753726951  x
5863243543011  x
073375326432  x
879001089010  x
697190726380  x
93335008008  x

The optimal assignment

Because there are 7 lines required, the zeros cover an optimal assignment:

4573708301719
8601753726951
5863243543011
073375326432
879001089010
697190726380
93335008008

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

5280809672426
9152564777456
69743852541122
8811489407240
889141790111
707294797391
953555882210

The optimal value equals 44.