# 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:

 19 93 28 63 84 40 74 99 31

Subtract row minima

We subtract the row minimum from each row:

 0 74 9 (-19) 23 44 0 (-40) 43 68 0 (-31)

Subtract column minima

We subtract the column minimum from each column:

 0 30 9 23 0 0 43 24 0 (-44)

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

 0 30 9 x 23 0 0 x 43 24 0 x

The optimal assignment

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

 0 30 9 23 0 0 43 24 0

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

 19 93 28 63 84 40 74 99 31

The optimal value equals 134.