What is one-dimensional cutting stock optimization?

The decision the optimizer makes

A job supplies stock lengths and quantities, required part lengths and quantities, plus process losses such as end trim and saw kerf. The solver selects how many stock bars to consume and which parts to cut from each one.

A cutting pattern is a repeatable recipe for one stock bar. Grouping identical patterns makes the output practical for a workshop rather than presenting a long list of individual bars.

How it differs from 2D nesting and bin packing

• 1D cutting optimizes length along bars, tubes, profiles or rolls.
• 2D nesting arranges shapes on sheets and must consider width, height, rotation and geometry.
• Bin packing commonly minimizes the number of containers; cutting stock often includes stock prices, finite inventory, kerf and trim.
• A useful production result must also prove that every demanded quantity is covered and every stock capacity constraint is respected.

A small concrete example

For 6000 mm stock with 8 mm trim at both ends and 3 mm kerf, the net length is not simply 6000 mm. Every selected pattern must reserve 16 mm for trim and account for the saw loss associated with its cuts. Omitting those losses can make a mathematically tidy pattern impossible on the machine.