# 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:

 96 14 93 56 91 59 95 38 35 98 68 15 78 46 1 28

Subtract row minima

We subtract the row minimum from each row:

 82 0 79 42 (-14) 53 21 57 0 (-38) 20 83 53 0 (-15) 77 45 0 27 (-1)

Subtract column minima

We subtract the column minimum from each column:

 62 0 79 42 33 21 57 0 0 83 53 0 57 45 0 27 (-20)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 62 0 79 42 x 33 21 57 0 x 0 83 53 0 x 57 45 0 27 x

The optimal assignment

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

 62 0 79 42 33 21 57 0 0 83 53 0 57 45 0 27

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

 96 14 93 56 91 59 95 38 35 98 68 15 78 46 1 28

The optimal value equals 88.