# 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:

 8 34 24 83 75 63 50 77 57 34 93 15 67 8 82 79

Subtract row minima

We subtract the row minimum from each row:

 0 26 16 75 (-8) 25 13 0 27 (-50) 42 19 78 0 (-15) 59 0 74 71 (-8)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 0 26 16 75 x 25 13 0 27 x 42 19 78 0 x 59 0 74 71 x

The optimal assignment

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

 0 26 16 75 25 13 0 27 42 19 78 0 59 0 74 71

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

 8 34 24 83 75 63 50 77 57 34 93 15 67 8 82 79

The optimal value equals 81.