# 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:

 85 80 71 4 61 52 23 95 2

Subtract row minima

We subtract the row minimum from each row:

 14 9 0 (-71) 0 57 48 (-4) 21 93 0 (-2)

Subtract column minima

We subtract the column minimum from each column:

 14 0 0 0 48 48 21 84 0 (-9)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

 14 0 0 x 0 48 48 x 21 84 0 x

The optimal assignment

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

 14 0 0 0 48 48 21 84 0

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

 85 80 71 4 61 52 23 95 2

The optimal value equals 86.