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:

667825583
352985834
1140894983
2424306999
694788230

Subtract row minima

We subtract the row minimum from each row:

617320078(-5)
272105026(-8)
029783872(-11)
0064575(-24)
650747826(-4)

Subtract column minima

We subtract the column minimum from each column:

617320052
27210500
029783846
0064549
65074780
(-26)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

617320052  x
27210500  x
029783846  x
0064549  x
65074780  x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

617320052
27210500
029783846
0064549
65074780

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

667825583
352985834
1140894983
2424306999
694788230

The optimal value equals 78.