# 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:

 89 36 6 69 72 47 34 31 40 33 23 7 8 80 8 50

Subtract row minima

We subtract the row minimum from each row:

 83 30 0 63 (-6) 41 16 3 0 (-31) 33 26 16 0 (-7) 0 72 0 42 (-8)

Subtract column minima

We subtract the column minimum from each column:

 83 14 0 63 41 0 3 0 33 10 16 0 0 56 0 42 (-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 83 14 0 63 x 41 0 3 0 x 33 10 16 0 x 0 56 0 42 x

The optimal assignment

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

 83 14 0 63 41 0 3 0 33 10 16 0 0 56 0 42

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

 89 36 6 69 72 47 34 31 40 33 23 7 8 80 8 50

The optimal value equals 68.