Wäscher Typology
The standard framework for classifying cutting & packing problems.
Also called: Wäscher Typology · Waescher typology · Cutting and packing typology · 절단 적재 유형론
Last verified: 2026-05-27
The standard framework that organizes the cutting & packing field (classified as
a concept in v1). Wäscher, Haußner & Schumann (2007) divide problems along four
criteria:
- Dimensionality — 1D, 2D, 3D, or more
- Kind of assignment — output maximization (maximize value packed into a fixed resource; knapsack-like) vs input minimization (accommodate all items while minimizing the resource used; bin-packing / cutting-stock-like)
- Assortment of small items — identical / weakly / strongly heterogeneous
- Assortment of large objects (bins/sheets) — one or several, identical or not
These combine into basic problem types such as knapsack, bin packing, cutting stock, and open-dimension (strip) problems. Many of OptAtlas's formal-problem nodes map onto a cell of this framework — e.g. 2D Bin Packing is input minimization, 2D Knapsack is output maximization.
Claims & evidence
Every relationship is a claim with an equivalence level and an evidence grade. See the evidence policy.
| Relationship | Claim | Equiv. | Evidence | Sources |
|---|---|---|---|---|
| mentions2D Bin Packing | The typology classifies 2D bin packing as an 'input minimization' type — accommodate all items while minimizing the bins used. | — | A |
|
| mentions2D Knapsack | The typology classifies 2D knapsack as an 'output maximization' type — maximize the value packed into a fixed resource. | — | A |
|
| mentions1D Cutting Stock | The typology classifies 1D cutting stock as an 'input minimization' type with strongly heterogeneous small items. | — | A |
|
Neighborhood
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