# 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:

 99 18 95 81 55 32 80 31 52

Subtract row minima

We subtract the row minimum from each row:

 81 0 77 (-18) 49 23 0 (-32) 49 0 21 (-31)

Subtract column minima

We subtract the column minimum from each column:

 32 0 77 0 23 0 0 0 21 (-49)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

 32 0 77 x 0 23 0 x 0 0 21 x

The optimal assignment

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

 32 0 77 0 23 0 0 0 21

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

 99 18 95 81 55 32 80 31 52

The optimal value equals 130.