Cutstock

Cutstock refers to the material stock used in manufacturing that is cut into pieces to meet product specifications. The term is used across several industries, including woodworking, metalworking, textiles, and printing. Cutstock management encompasses selecting appropriate stock sizes, planning the cutting operations, and handling trim waste. The phrase can also describe the cutting process itself and the resulting waste.

In operations research, the cutting stock problem is a formal optimization problem. Given standard-size stock (a roll, sheet, or bar) and a set of required item sizes with quantities, determine cutting patterns to satisfy demand while minimizing waste and the number of stock units used. The problem is studied in one dimension (lengths) and, in some contexts, in two dimensions (areas) where patterns may be guillotine (straight-line cuts) or non-guillotine.

Key concepts include stock length or area, demand for various item sizes, and a finite set of feasible cutting patterns. The objective is typically to minimize waste or stock usage while meeting all demand constraints. Patterns are combined to form feasible solutions, often represented in a linear or integer programming framework.

Solution methods range from exact to heuristic. Exact approaches use integer programming with column generation, notably the Gilmore–Gomory method, to handle large pattern sets. Heuristics and metaheuristics (greedy algorithms, clustering, genetic algorithms, simulated annealing) provide good solutions quickly for complex or large-scale instances. In practice, problem variants (pattern generation, two-dimensional cutting, rotation constraints) shape the chosen method.

Applications span printing, textiles, leather goods, metal fabrication, woodworking, and paper industries. The cutstock framework informs production planning, inventory management, and waste reduction strategies, contributing to cost efficiency and material conservation.