# 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:

 64 90 9 42 15 55 33 58 25 26 17 91 58 53 18 17

Subtract row minima

We subtract the row minimum from each row:

 55 81 0 33 (-9) 0 40 18 43 (-15) 8 9 0 74 (-17) 41 36 1 0 (-17)

Subtract column minima

We subtract the column minimum from each column:

 55 72 0 33 0 31 18 43 8 0 0 74 41 27 1 0 (-9)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 55 72 0 33 x 0 31 18 43 x 8 0 0 74 x 41 27 1 0 x

The optimal assignment

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

 55 72 0 33 0 31 18 43 8 0 0 74 41 27 1 0

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

 64 90 9 42 15 55 33 58 25 26 17 91 58 53 18 17

The optimal value equals 67.