The cutting stock problem, explained

The cutting stock problem asks: given stock of fixed lengths and a list of shorter pieces you need, how do you cut them so you use the least material? In one dimension — cutting lengths from bars or boards — it's a close cousin of the bin packing problem, where you pack items into as few bins as possible.

It shows up anywhere material is cut to length: steel service centers, sawmills, glass and paper converting, even cable cutting. The names change; the underlying problem doesn't.

With a handful of cuts you could try every arrangement by hand. But the number of possible layouts explodes as the cut list grows — for a real job it's astronomically large, far beyond checking one by one. The problem is NP-hard, meaning no known method finds the guaranteed-best answer quickly for every input.

That's why eyeballing a cut list rarely produces the tightest plan, and why the savings from a tool are real rather than marginal.

Because finding the perfect answer is impractical, good optimizers use heuristics — fast strategies that get very close to optimal. First-Fit-Decreasing and Best-Fit-Decreasing, which sort parts largest-first and slot each into the best available stock, are classic examples.

NestSolver runs more than one strategy and keeps whichever produces the least waste for your specific cut list, then accounts for kerf and blocked zones on top. You get a near-optimal plan in seconds instead of an exact one never.

Not at all. The point of a cut optimizer is that the hard part is handled for you: you enter stock and parts, and it returns a layout. The theory just explains why the tool beats cutting by feel.

If you want to see it work, NestSolver's optimizer is free and needs no sign-up — enter a cut list and watch it nest the parts onto the fewest pieces.