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:

99915821
67241567
5190241
35749376

Subtract row minima

We subtract the row minimum from each row:

7870370(-21)
529052(-15)
4988039(-2)
0395841(-35)

Subtract column minima

We subtract the column minimum from each column:

7861370
520052
4979039
0305841
(-9)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

7861370  x
520052  x
4979039  x
0305841  x

The optimal assignment

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

7861370
520052
4979039
0305841

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

99915821
67241567
5190241
35749376

The optimal value equals 82.