Wäscher Typology

The standard framework for classifying cutting & packing problems.

Also called: Wäscher Typology · Waescher typology · Cutting and packing typology · 절단 적재 유형론

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 evidence grade; applicable problem-to-problem relationships also carry an equivalence level. See the evidence policy.

A–X describes evidence reliability; E0–E4 describes mathematical similarity between problems. The two axes are independent.

Relationships from this entry 3

mentions
Wäscher Typology to 2D Bin Packing
The typology classifies 2D bin packing as an 'input minimization' type — accommodate all items while minimizing the bins used.
EvidenceA · Peer-reviewed / official
Sources
- Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems
  Citation details
  Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
mentions
Wäscher Typology to 2D Knapsack
The typology classifies 2D knapsack as an 'output maximization' type — maximize the value packed into a fixed resource.
EvidenceA · Peer-reviewed / official
Sources
- Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems
  Citation details
  Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
mentions
Wäscher Typology to 1D Cutting Stock
The typology classifies 1D cutting stock as an 'input minimization' type with strongly heterogeneous small items.
EvidenceA · Peer-reviewed / official
Sources
- Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems
  Citation details
  Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.

Relationships from this entry
Relationship	Claim	Evidence	Equiv.	Sources
mentions Wäscher Typology to 2D Bin Packing	The typology classifies 2D bin packing as an 'input minimization' type — accommodate all items while minimizing the bins used.	A · Peer-reviewed / official	—	Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems Citation details Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
mentions Wäscher Typology to 2D Knapsack	The typology classifies 2D knapsack as an 'output maximization' type — maximize the value packed into a fixed resource.	A · Peer-reviewed / official	—	Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems Citation details Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
mentions Wäscher Typology to 1D Cutting Stock	The typology classifies 1D cutting stock as an 'input minimization' type with strongly heterogeneous small items.	A · Peer-reviewed / official	—	Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems Citation details Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.