Need help with a cutting stock problem

Factual Questions
1

My mom called me up tonight and was looking for a solution to her problem for her business that needs wood cut for the widget she’s making.

She is buying lengths of pole at 14’ (168") each and needs the following lengths cut
2 @ 40"
2 @ 33"
2 @ 46"
2 @ 35"

I saw a formula for this on Wikipedia but it’s far out of my skillset to figure out.

Any help out there?

2

As long as you don’t try to cut all the big pieces from one pole, you’ll be OK. For example, one of each length from each pole will work:
46+40+35+33 = 154 from each pole.

There’s not much opportunity for any savings here, even if you were making a bunch of copies.

Don’t just mark them all off at the beginning and then start cutting. The saw will remove some width of wood, maybe 1/8 inch.

3

You only need 2 poles doing it as ZenBeam suggests. Worst case you need 3 poles.

4

As ZenBeam notes, it’s quite easy to make this work with 2 poles. The following scheme leaves you with the longest possible piece left over:
Pole 1: 46 + 46 + 40 + 35 leaves 1" (less 3 saw kerfs)
Pole 2: 40 + 35 + 33 + 33 leaves 27" (less 3 saw kerfs)

5

Thanks all!

6

Here’s a gross simplification of the formulas described on the wikipedia article you linked to:

  1. determine what the waste is for each possible stock cutting pattern
  2. determine what combination of patterns (could be the same one multiple times) will meet your production requirements
  3. calculate the total waste is for each pattern combination.

Which is probably not what you were looking for.
The reason the math looks so hairy is because it’s not an actual formula, it just states how the factors limit the possible solutions.