# 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:

 40 58 92 11 44 9 23 86 5 18 86 67 67 75 45 76

Subtract row minima

We subtract the row minimum from each row:

 29 47 81 0 (-11) 35 0 14 77 (-9) 0 13 81 62 (-5) 22 30 0 31 (-45)

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:

 29 47 81 0 x 35 0 14 77 x 0 13 81 62 x 22 30 0 31 x

The optimal assignment

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

 29 47 81 0 35 0 14 77 0 13 81 62 22 30 0 31

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

 40 58 92 11 44 9 23 86 5 18 86 67 67 75 45 76

The optimal value equals 70.