# 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):

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

 87 32 48 24 46 2 5 64 17

Subtract row minima

We subtract the row minimum from each row:

 55 0 16 (-32) 22 44 0 (-2) 0 59 12 (-5)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

 55 0 16 x 22 44 0 x 0 59 12 x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

 55 0 16 22 44 0 0 59 12

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

 87 32 48 24 46 2 5 64 17

The optimal value equals 39.