Waste planning

The blend scheduling deals with the problem, a predetermined length (a dimension planning), a predetermined area (planning of two dimensions ) or a predetermined space (planning of three dimensions) divided into specific sub-areas.

Basics

The aim of waste planning is, on the one hand, to maintain the desired dimensions of the sub-areas and, on the other, to minimize the so-called waste: The remaining remaining areas should be minimal in order to reduce waste costs. Specific applications are for example:

• One-dimensional problems : cutting of required pipe sections from standard pipes.
• Two-dimensional problems: cutting pieces of fabric from raw material, punching out shaped sheets from standard sheets.
• three-dimensional problems: loading a cargo hold / container with packages, cutting out molded parts from raw material blocks.

In addition to a number of different target definitions (minimizing the waste, avoiding falling short of certain minimum sizes of the leftover pieces, etc.), waste planning knows a number of other restrictions when finding a solution: For example, a pattern must be taken into account for fabric cuts; for wood cuts, the grain direction in which Freight loading, the weight distribution, with laser cuts made of sheet steel, a minimum distance between the workpieces. These specifications have a significant influence on the quality of the solution, because z. B. the possible rotations of an object on the surface or any positioning in space can be restricted.

For most one-dimensional problems, algorithms are known that lead to optimal solutions within reasonable computing times. This also applies to two-dimensional problems, as long as they only aim at simply shaped surfaces (e.g. rectangles). For surfaces of any shape ( polygons ), the search for the optimal solution is usually not an option for practical problems due to the required computing time. In this case, heuristics are used that deliver a solution of sufficient quality, but which may be below the theoretical optimum. If, in the case of complex problems, a high quality solution is required (e.g. with very expensive raw materials), a manually supported solution determination can definitely be economical: a heuristic gives an experienced user the intermediate results graphically so that he can make certain corrections "intuitively" and can influence the further calculation process in a targeted manner.

Waste calculation

The waste calculation is used to calculate the waste, for example when laying, e.g. B. of carpets . One distinguishes between

1. Offcuts
2. Waste surcharge

depending on whether you start with the raw material or the finished material. This results in the cutoff rate V _ab and the cut allowance rate V _to .

The following applies in both cases:

Blended quantity (VM) = raw quantity (RM) - finished quantity (FM)

or analogously for surfaces

Scrap = starting area - development area

Offcut discount calculation

During the manufacturing process (e.g. in production), the waste (VM) is determined using the waste discount calculation . The raw quantity (RM) is set to 100%:

${\displaystyle V_{ab}={\frac {RM-FM}{RM}}\cdot 100\,\%}$

${\displaystyle VM={\frac {V_{ab}\cdot RM}{100\,\%}}}$

${\displaystyle FM=RM\cdot \left(1-{\frac {V_{ab}}{100\,\%}}\right)}$

Off-cut allowance calculation

In the waste overhead calculation (. Eg in the calculation), in which the finished volume (FM) = corresponds to 100%, which is blended (VM) of Finished amount (FM) slammed percentage:

${\displaystyle V_{zu}={\frac {RM-FM}{FM}}\cdot 100\,\%}$

${\displaystyle VM={\frac {V_{zu}\cdot FM}{100\,\%}}}$

${\displaystyle RM=FM\cdot \left(1+{\frac {V_{zu}}{100\,\%}}\right)}$

example

The largest possible circular area should be cut from a square area. How big is the waste surcharge or the waste reduction?

${\displaystyle RM=a^{2}}$

${\displaystyle FM=a^{2}\cdot {\frac {\pi }{4}}}$

${\displaystyle VM=a^{2}\cdot \left(1-{\frac {\pi }{4}}\right)}$

${\displaystyle V_{ab}=21{,}46\,\%}$

${\displaystyle V_{zu}=27{,}32\,\%}$

See also

• Parquet - the mathematical theory of the waste-free division of an area into similar parts
• One-dimensional cutting problem - the problem one dimension simpler.