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:

76871330
66481642
438137
85334964

Subtract row minima

We subtract the row minimum from each row:

6374017(-13)
5032026(-16)
427036(-1)
5201631(-33)

Subtract column minima

We subtract the column minimum from each column:

217400
83209
07019
1001614
(-42)(-17)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

217400  x
83209  x
07019  x
1001614  x

The optimal assignment

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

217400
83209
07019
1001614

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

76871330
66481642
438137
85334964

The optimal value equals 122.