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:

28565846
80323264
17628735
26134185

Subtract row minima

We subtract the row minimum from each row:

0283018(-28)
480032(-32)
0457018(-17)
1302872(-13)

Subtract column minima

We subtract the column minimum from each column:

028300
480014
045700
1302854
(-18)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

028300  x
480014  x
045700  x
1302854  x

The optimal assignment

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

028300
480014
045700
1302854

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

28565846
80323264
17628735
26134185

The optimal value equals 108.