An algorithm for corrugated paper cutting

An automated machine cuts the rolls of corrugated paper longitudinally and splits the paper stripe into multiple conveyors, where in each of them a different equidistant lateral cut can be applied. There is a choice of input rolls of infinite length but different widths. The market requirement for large series of different rectangle-shaped articles has to be met. Upper limits for the articles also exist. The minimum material consumption is the objective of optimisation. A recursive function to generate all the possible cutting schemas is written. It provides for formulation of a linear programming model. The minimisation of machine set-up costs cannot be practically solved by binary variables because of the prohibitive problem size. Instead, an iterative navigation around the achieved optimum solution, using the dual activity values is devised. Key-Words: Cutting stock problem, Linear programming, Integer programming, Production planning, Duality