# 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:

 62 52 20 18 19 91 24 97 45 95 59 28 79 33 63 21

Subtract row minima

We subtract the row minimum from each row:

 44 34 2 0 (-18) 0 72 5 78 (-19) 17 67 31 0 (-28) 58 12 42 0 (-21)

Subtract column minima

We subtract the column minimum from each column:

 44 22 0 0 0 60 3 78 17 55 29 0 58 0 40 0 (-12) (-2)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 44 22 0 0 x 0 60 3 78 x 17 55 29 0 x 58 0 40 0 x

The optimal assignment

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

 44 22 0 0 0 60 3 78 17 55 29 0 58 0 40 0

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

 62 52 20 18 19 91 24 97 45 95 59 28 79 33 63 21

The optimal value equals 100.