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:

3775347
63883527
87632130
9891343

Subtract row minima

We subtract the row minimum from each row:

0745044(-3)
366180(-27)
664209(-21)
890434(-9)

Subtract column minima

Because each column contains a zero, subtracting column minima has no effect.

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0745044  x
366180  x
664209  x
890434  x

The optimal assignment

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

0745044
366180
664209
890434

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

3775347
63883527
87632130
9891343

The optimal value equals 60.