OptAtlas
Formal problem

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 4×44\times4 panel, a horizontal edge-to-edge cut splits it into 4×14\times1 and 4×34\times3; a vertical cut then divides the 4×34\times3 into two 2×32\times3 — 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

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Claims & evidence

Every relationship is a claim with an equivalence level and an evidence grade. See the evidence policy.

RelationshipClaimEquiv.EvidenceSources
variant of2D Bin PackingGuillotine cutting is a variant of 2D orthogonal cutting & packing with the added constraint that cuts must be edge-to-edge and straight.E1A
  • AAn improved typology of cutting and packing problems
uses methodDynamic ProgrammingGuillotine patterns, thanks to their recursive subdivision structure, can be handled efficiently with dynamic programming (Gilmore–Gomory).A
  • AMultistage Cutting Stock Problems of Two and More Dimensions
shares method with2D Strip PackingGuillotine cutting and strip packing share orthogonal placement methodology.E2B
  • AAn improved typology of cutting and packing problems
uses methodColumn GenerationGilmore & Gomory extended the column-generation / pattern-generation approach to two-dimensional guillotine cutting stock.A
  • AMultistage Cutting Stock Problems of Two and More Dimensions
uses methodGenetic AlgorithmGuillotine cutting / panel cutting has also been addressed with metaheuristics such as genetic algorithms.B
  • ATwo-dimensional packing problems: A survey
uses methodBranch and BoundExact approaches to guillotine cutting have been reported with branch and bound.B
  • ATwo-dimensional packing problems: A survey
shares method with2D KnapsackMaximizing on a single sheet under the guillotine constraint is the guillotine 2D knapsack, sharing methodology with 2D knapsack.E2B
  • AAn improved typology of cutting and packing problems
adjacent benchmark2DPackLibSome orthogonal instances in 2DPackLib relate to guillotine variants, making it an adjacent benchmark.B
  • A2DPackLib: a two-dimensional cutting and packing library

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See also

Not directly linked, but conceptually close — by the connections and descriptions they share.