Guillotine Cutting
Orthogonal cutting constrained to edge-to-edge straight cuts.
Also called: Guillotine Cutting · 길로틴 컷 · Guillotine-cut packing
Last verified: 2026-05-27
Definition
A cutting & packing problem where rectangles are cut or placed under the constraint that each cut runs straight from one edge of the current piece to the opposite edge.
Example
From a panel, a horizontal edge-to-edge cut splits it into and ; a vertical cut then divides the into two — each cut runs edge to edge, satisfying the guillotine constraint. By contrast, a “pinwheel” arrangement, where one piece is boxed in at the center, cannot be separated by any single straight cut and so is not guillotine-producible.
Why it matters
The guillotine constraint is not arbitrary — many cutting machines (panel saws, glass cutters, paper guillotines) can only make edge-to-edge straight cuts. This recursive structure fits dynamic programming well.
Related nodes
See the depth-1 graph below.
Claims & evidence
Every relationship is a claim with an equivalence level and an evidence grade. See the evidence policy.
| Relationship | Claim | Equiv. | Evidence | Sources |
|---|---|---|---|---|
| variant of2D Bin Packing | Guillotine cutting is a variant of 2D orthogonal cutting & packing with the added constraint that cuts must be edge-to-edge and straight. | E1 | A |
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| uses methodDynamic Programming | Guillotine patterns, thanks to their recursive subdivision structure, can be handled efficiently with dynamic programming (Gilmore–Gomory). | — | A |
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| shares method with2D Strip Packing | Guillotine cutting and strip packing share orthogonal placement methodology. | E2 | B |
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| uses methodColumn Generation | Gilmore & Gomory extended the column-generation / pattern-generation approach to two-dimensional guillotine cutting stock. | — | A |
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| uses methodGenetic Algorithm | Guillotine cutting / panel cutting has also been addressed with metaheuristics such as genetic algorithms. | — | B |
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| uses methodBranch and Bound | Exact approaches to guillotine cutting have been reported with branch and bound. | — | B |
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| shares method with2D Knapsack | Maximizing on a single sheet under the guillotine constraint is the guillotine 2D knapsack, sharing methodology with 2D knapsack. | E2 | B |
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| adjacent benchmark2DPackLib | Some orthogonal instances in 2DPackLib relate to guillotine variants, making it an adjacent benchmark. | — | B |
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Neighborhood
Direct graph neighbors. Toggle depth to expand.
See also
Not directly linked, but conceptually close — by the connections and descriptions they share.
- 2D Irregular NestingFormal problem4 connections in common
- 3D Bin PackingFormal problem3 connections in common
- Integer Linear ProgrammingMethod3 connections in common
- 0/1 Knapsack ProblemFormal problem3 connections in common
- 1D Cutting StockFormal problem3 connections in common
- Pallet LoadingFormal problem3 connections in common