# 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:

 62 69 95 26 73 65 98 11 79

Subtract row minima

We subtract the row minimum from each row:

 0 7 33 (-62) 0 47 39 (-26) 87 0 68 (-11)

Subtract column minima

We subtract the column minimum from each column:

 0 7 0 0 47 6 87 0 35 (-33)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

 0 7 0 x 0 47 6 x 87 0 35 x

The optimal assignment

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

 0 7 0 0 47 6 87 0 35

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

 62 69 95 26 73 65 98 11 79

The optimal value equals 132.