Blend planning concerns itself with the problem, a given length (planning of a dimension), a given surface (planning of two dimensions) to divide or a given area (planning of three dimensions) into certain subranges. A goal is thereby on the one hand the adherence to the desired dimensions of the subranges, on the other hand the minimization of the so-called blend: The remaining remainder ranges should be minimal, in order to reduce the blend costs. Concrete applications are for example:

1-dimensionale of problems: Cut from necessary pipes from standard pipes.

two-dimensional problems: Cut from pieces of material from raw material, a punching out of shaped plates out of standard sheet metals.

three-dimensional problems: Load a cargo/a container with packages, a cutting out of shaped parts of raw material blocks.

Blend planning knows a set of further restrictions beside a set of different goal definitions (minimization of the blend, avoidance of falling below of certain minimum sizes of the remaining pieces etc.) during the solution identification: With material cuts for example a sample must be considered, with wood cuts the fiber direction, during the freight loading the weight distribution, with laser cuts from steel sheet a minimum distance between the workpieces. These defaults have substantial influence on the solution quality, because thereby the possible turns of an object on the surface or the arbitrary positioning in the area are e.g. limited.

For most 1-dimensionalen problems are algorithms well-known, which lead within justifiable computing times to optimal solutions. This applies likewise to two-dimensional problems, so long these only simply formed surfaces (e.g. Rectangles) to the goal have. For surfaces (Polygone), at will formed, the search for the optimal solution is not usually possible due to the necessary computing time for practical problems. In this case heuristics are used, which supply a solution with sufficient quality, which lies however below the theoretical optimum. In case of complex problems if a high solution quality is needed (e.g. with very expensive raw materials), a manually supported solution determination can quite become economical: A heuristic gives the intermediate results to an experienced user graphically prepared, so that this can "intuitively" certain corrections make and the further computing process purposefully affect can.

Blend computation

The blend computation serves for it, the blend for example with the transfer, e.g. from carpets to determine. One differentiates between

1. Blend anticipated payment and
2. Blend addition,

according to whether one proceeds with the raw material or from the finished material. Therefore the blend anticipated payment set of Vab and the blend costing rate Vzu result.

Hereunder applies in both cases:

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

or similar for surfaces

Blend = output surface - completion surface

A. With the production process (e.g. in the manufacturing) the blend (VM) is determined over the blend anticipated payment calculation. Here the raw quantity (RM) is set = 100%:

V_ {off} = \ frac {RM-FM} {RM} \ cdot100 \ %

VM= \ frac {V_ {} \ cdot off RM} {100 \ %}

FM=RM \ cdot \ left (1 \ frac {V_ {off}} {100 \ %} \ right)

b. During the blend addition calculation (e.g. in the calculation), with which the finished quantity (FM) = 100% corresponds, the blend (VM) of the finished quantity (FM) proportionally one slams shut:

V_ {too} = \ frac {RM-FM} {FM} \ cdot100 \ %

VM= \ frac {V_ {too} \ cdot FM} {100 \ %}

RM=FM \ cdot \ left (1+ \ frac {V_ {too}} {100 \ %} \ right)

Example

From a square surface the greatest possible circular area is to be cut. Is the blend addition and/or the blend anticipated payment how

RM=a^2

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

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

V_ {off} = 21 {,} 46 \ %

V_ {too} = 27 {,} 32 \ %

Articles in category "Blend planning"

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