# 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:

 52 54 51 34 67 77 47 17 88

Subtract row minima

We subtract the row minimum from each row:

 1 3 0 (-51) 0 33 43 (-34) 30 0 71 (-17)

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 3 lines required to cover all zeros:

 1 3 0 x 0 33 43 x 30 0 71 x

The optimal assignment

Because there are 3 lines required, the zeros cover an optimal assignment:

 1 3 0 0 33 43 30 0 71

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

 52 54 51 34 67 77 47 17 88

The optimal value equals 102.