The Cutting Stock Problem, Explained Simply
What the cutting stock problem is, why it is NP-hard, and how 1D and 2D optimizers (guillotine vs true nesting) find good solutions fast.
What is the cutting stock problem?
Given stock lengths (bars, boards, sheets) and a list of requested pieces, cut all pieces from as little stock as possible. It sounds trivial; mathematically it is NP-hard — the number of combinations explodes as the piece list grows.
1D, 2D and guillotine cuts
1D means one dimension: pipes, profiles, studs. 2D adds width — plywood, glass, sheet metal. Guillotine cuts run edge to edge (what a panel saw does); true nesting allows any rotation and non-guillotine layouts (what lasers and routers do).
Why exact solutions are rare
Only small instances can be solved exactly (dynamic or integer programming). Industry relies on heuristics — First Fit Decreasing, Best Fit Decreasing, shelf algorithms — which usually land within a few percent of the optimum in milliseconds.
Kerf and other real-world traps
Every cut consumes material: a 3 mm blade kerf adds 3 mm per cut, and 50 cuts silently eat 150 mm of stock. Offcut reuse, grain direction and trim losses matter just as much as the packing itself.
Try it on your own cut list
The Linear cutting calculator optimizes bar and profile lists; the Sheet cutting calculator handles guillotine sheet layouts with rotation and kerf. Paste your list and compare total stock before and after.
Linear cutting calculator Open the linear cutting calculator