# 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:

 5 42 59 25 54 85 41 99 14 75 40 41 56 21 19 84

Subtract row minima

We subtract the row minimum from each row:

 0 37 54 20 (-5) 13 44 0 58 (-41) 0 61 26 27 (-14) 37 2 0 65 (-19)

Subtract column minima

We subtract the column minimum from each column:

 0 35 54 0 13 42 0 38 0 59 26 7 37 0 0 45 (-2) (-20)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 0 35 54 0 x 13 42 0 38 x 0 59 26 7 x 37 0 0 45 x

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

 0 35 54 0 13 42 0 38 0 59 26 7 37 0 0 45

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

 5 42 59 25 54 85 41 99 14 75 40 41 56 21 19 84

The optimal value equals 101.