Cutting Stock

When the user wants to solve one-dimensional cutting stock problems — cutting demanded item widths from standard stock rolls at minimum roll usage or trim loss — with pattern-based (Gilmore-Gomory) or compact MIP models, column generation with knapsack pricing, and integer rounding. Also use when the user mentions "cutting stock," "trim loss," "cutting patterns," "stock rolls," "pattern generation," "Gilmore-Gomory," or when a covering model has one column per feasible cutting pattern. For the generic restricted-master/pricing machinery, see column-generation; for the unit-demand cousin of this problem, see bin-packing.