# 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:

 17 1 10 64 56 71 81 4 36 34 2 61 82 10 90 13

Subtract row minima

We subtract the row minimum from each row:

 16 0 9 63 (-1) 52 67 77 0 (-4) 34 32 0 59 (-2) 72 0 80 3 (-10)

Subtract column minima

We subtract the column minimum from each column:

 0 0 9 63 36 67 77 0 18 32 0 59 56 0 80 3 (-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 0 0 9 63 x 36 67 77 0 x 18 32 0 59 x 56 0 80 3 x

The optimal assignment

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

 0 0 9 63 36 67 77 0 18 32 0 59 56 0 80 3

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

 17 1 10 64 56 71 81 4 36 34 2 61 82 10 90 13

The optimal value equals 33.