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:

6119477
10716018
36348382
70141354

Subtract row minima

We subtract the row minimum from each row:

058871(-6)
061508(-10)
204948(-34)
571041(-13)

Subtract column minima

We subtract the column minimum from each column:

058863
061500
204940
571033
(-8)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

058863  x
061500  x
204940  x
571033  x

The optimal assignment

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

058863
061500
204940
571033

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

6119477
10716018
36348382
70141354

The optimal value equals 71.