# 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:

 62 77 96 64 42 82 69 30 75 47 11 31 44 9 93 26

Subtract row minima

We subtract the row minimum from each row:

 0 15 34 2 (-62) 12 52 39 0 (-30) 64 36 0 20 (-11) 35 0 84 17 (-9)

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 15 34 2 x 12 52 39 0 x 64 36 0 20 x 35 0 84 17 x

The optimal assignment

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

 0 15 34 2 12 52 39 0 64 36 0 20 35 0 84 17

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

 62 77 96 64 42 82 69 30 75 47 11 31 44 9 93 26

The optimal value equals 112.