Calculating a cutting list with the least amount of off cut waste

This is a classic, difficult problem to solve efficiently. The algorithm you describe sounds like a Greedy Algorithm. Take a look at this Wikipedia article for more information: The Cutting Stock Problem

No specific ideas on this problem, I'm afraid - but you could look into a 'genetic algorithm' (which would go something like this)...

Place the lengths to cut in a random order and give that order a score based on how good a match it is to your ideal solution (0% waste, presumably).

Then, iteratively make random alterations to the order and re-score it. If the score is higher, ditch the result. If the score is lower, keep it and use it as the basis for your next calculation. Keep going until you get your score within acceptable limits.

What you described is indeed classified as a Cutting Stock problem, as Wheelie mentioned, and not a Bin Packing problem because you try to minimize the waste (sum of leftovers) rather than the number of extrusions used.

Both of those problems can be very hard to solve, but the 'best fit' algorithm you mentioned (using the longest 'small length' that fits the current extrusion) is likely to give you very good answers with a very low complexity.

Actually, since the size of material is fixed, but the requests are not, it's a bin packing problem.

Again, wikipedia to the rescue!

(Something I might have to look into for work too, so yay!)

That's an interesting problem because I suppose it depends on the quantity of each length you're producing. If they are all the same quantity and you can get Each different length onto one 5m extrusion then you have the optimum soloution.

However if they don't all fit onto one extrusion then you have a greater problem. To keep the same amount of cuts for each length you need to calculate how many lengths (not necessarily in order) can fit on one extrusion and then go in an order through each extrusion.