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:

64754281
65878152
237225
79783974

Subtract row minima

We subtract the row minimum from each row:

2233039(-42)
1335290(-52)
035023(-2)
4039035(-39)

Subtract column minima

We subtract the column minimum from each column:

220039
132290
02023
406035
(-33)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

220039  x
132290  x
02023  x
406035  x

The optimal assignment

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

220039
132290
02023
406035

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

64754281
65878152
237225
79783974

The optimal value equals 168.