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:

9726519
93391558
83597365
76214470

Subtract row minima

We subtract the row minimum from each row:

8817420(-9)
7824043(-15)
240146(-59)
5502349(-21)

Subtract column minima

We subtract the column minimum from each column:

6417420
5424043
00146
3102349
(-24)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

6417420  x
5424043  x
00146  x
3102349  x

The optimal assignment

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

6417420
5424043
00146
3102349

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

9726519
93391558
83597365
76214470

The optimal value equals 128.