# 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:

 79 3 96 22 48 37 39 19 22 56 38 38 75 57 71 93

Subtract row minima

We subtract the row minimum from each row:

 76 0 93 19 (-3) 29 18 20 0 (-19) 0 34 16 16 (-22) 18 0 14 36 (-57)

Subtract column minima

We subtract the column minimum from each column:

 76 0 79 19 29 18 6 0 0 34 2 16 18 0 0 36 (-14)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 76 0 79 19 x 29 18 6 0 x 0 34 2 16 x 18 0 0 36 x

The optimal assignment

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

 76 0 79 19 29 18 6 0 0 34 2 16 18 0 0 36

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

 79 3 96 22 48 37 39 19 22 56 38 38 75 57 71 93

The optimal value equals 115.