Linear Cutting Overview.

Cutting of any one-dimension (1D) stock material (bars, pipes, wires, etc.) is widely used by handymen, hobbyists and professionals. Cutting the baseboards for the home renovation or cutting the paper rolls at the factory have one common purpose – minimize the waste and quantity of used stocks and therefore reduce the cost of the project.

The problem statement is very simple – there are linear stocks with their length, quantity and cost and there are parts that have to be cut from the stocks. Parts are defined by their lengths and quantity. The purposes of the calculation are following:

• Define the length and quantity of the stocks required to cut all parts.
• Generate the parts location layout which indicates the stock and the coordinate of every part.
• Generate the sequence and the coordinates of the cuts for each layout.
• Utilize as much as possible of the cheaper stocks and therefore minimize the total project cost.

Sometimes the cutting involves knives or saws and the latest case the saw kerf (thickness) has to be taken into consideration during the optimization. Another variety is incomplete optimization when the stock supply is limited and only some parts can be cut from the stocks.

It's hard to solve the cutting problem manually therefore there are lot of specialized optimization software application on the market that can do it automatically.