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):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

14712199
64912497
7220373
9911839

Subtract row minima

We subtract the row minimum from each row:

057785(-14)
4067073(-24)
6917340(-3)
913031(-8)

Subtract column minima

We subtract the column minimum from each column:

054785
4064073
6914340
910031
(-3)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

054785  x
4064073  x
6914340  x
910031  x

The optimal assignment

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

054785
4064073
6914340
910031

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

14712199
64912497
7220373
9911839

The optimal value equals 52.