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:

99484037
69574479
20257863
29907336

Subtract row minima

We subtract the row minimum from each row:

621130(-37)
2513035(-44)
055843(-20)
061447(-29)

Subtract column minima

We subtract the column minimum from each column:

62630
258035
005843
056447
(-5)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

62630  x
258035  x
005843  x
056447  x

The optimal assignment

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

62630
258035
005843
056447

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

99484037
69574479
20257863
29907336

The optimal value equals 135.