Setup minimising conditions in the trim loss problem

The one-dimensional cutting stock, trim or deckling problem arises in cutting short units from long ones. The long units could be pipes, rods or reels of paper. The objectives are to fill demand with as little stock as possible, to reduce trim waste and to keep the number of setups to a minimum. We examine a formal approach to setup minimization and show that, at best, it provides necessary conditions for solving this task. Sufficient conditions also required the generation of all possible patterns, in principle at least.