# 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:

 88 44 55 44 80 64 63 51 6

Subtract row minima

We subtract the row minimum from each row:

 44 0 11 (-44) 0 36 20 (-44) 57 45 0 (-6)

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:

 44 0 11 x 0 36 20 x 57 45 0 x

The optimal assignment

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

 44 0 11 0 36 20 57 45 0

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

 88 44 55 44 80 64 63 51 6

The optimal value equals 94.