How calculate minimal waste when tailoring tubes

Question

I have a rather mathematical problem I need to solve:

The task is to cut a predefined number of tubes out of fixed length tubes with a minimum amount of waste material.

So let's say I want to cut 10 1m tubes and 20 2,5m tubes out of tubes with a standardized length of 6m.

I'm not sure what an algorithm for this kind of problem would look like?

I was thinking to create a list of variations of the different sized tubes, fit them into the standard sized tubes and then choose the variation with the minimal waste.

First I'm not sure if there are not other and better ways to attack the problem.

Second I did not find a solution HOW I would create such a variations list.

Any help is greatly appreciated, thanks!

Answer 1

This is known as the Cutting Stock problem. Wikipedia has a number of references that might help you find clues to an algorithm that works.

Answer 2

I believe you are describing the cutting stock problem. Some additional information and an online solver can be found here.