Geometry and linear footage calculations

[leetercola]

Geometry and linear footage calculations
I'm re-writing an application that takes x amount of pieces and tries to fit them best to the right number and size of stock material. EG: (So given 2 pieces at one size 1 at a larger size and 3 at a larger size find the most efficient cuts from the stock material.)

My Problem:
The way we currently handle this is to calculate linear footage and then step through a piece array, twice. Attempting to match the footage of the piece to the smallest core we can, along with as many other pieces possibly. I would like to optimize this as much as possible, and I'm wondering if there is some sort of equation to figure this out. I did a few searches but its hard to know what to search for.

I apologize for not being able to post code, but its long and messy anyways. Any help is appreciated. The section in question is 567 lines.

Relevant Info:
Core materials come in lengths of 144, 120, 96, 48.

[GeoRanger]

Do either of these links help?

The Bin-Packing Problem http://mathworld.wolfram.com/Bin-PackingProblem.html
The Knapsack Problem http://en.wikipedia.org/wiki/Knapsack_problem

No way is known to efficiently compute a best answer when confronted with these problems.