# 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:

 68 61 91 10 86 90 70 78 76 94 52 87 77 33 77 76

Subtract row minima

We subtract the row minimum from each row:

 58 51 81 0 (-10) 16 20 0 8 (-70) 24 42 0 35 (-52) 44 0 44 43 (-33)

Subtract column minima

We subtract the column minimum from each column:

 42 51 81 0 0 20 0 8 8 42 0 35 28 0 44 43 (-16)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

 42 51 81 0 x 0 20 0 8 x 8 42 0 35 x 28 0 44 43 x

The optimal assignment

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

 42 51 81 0 0 20 0 8 8 42 0 35 28 0 44 43

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

 68 61 91 10 86 90 70 78 76 94 52 87 77 33 77 76

The optimal value equals 181.