Approaches to real world two-dimensional cutting problems

• We propose fast heuristics, Integer Linear Programming models and a truncated Branch-and-Price algorithm for a wooden board Cutting Stock Problem.
• We explicitly consider the maximization of the cutting equipment productivity, which can be obtained by cutting identical boards in parallel.
• This objective is in conflict with the traditional objective of trim loss minimization, thus defining a multi-objective optimization problem.
• We perform computational experiments on a set of realistic instances from the industry.
• Experiments show that the productivity can be improved with a minimal increase in the total area of used boards.

We consider a real world generalization of the 2-Dimensional Guillotine Cutting Stock Problem arising in the wooden board cutting industry. A set of rectangular items has to be cut from rectangular stock boards, available in multiple formats. In addition to the classical objective of trim loss minimization, the problem also asks for the maximization of the cutting equipment productivity, which can be obtained by cutting identical boards in parallel. We present several heuristic algorithms for the problem, explicitly considering the optimization of both objectives. The proposed methods, including fast heuristic algorithms, Integer Linear Programming models and a truncated Branch and Price algorithm, have increasing complexity and require increasing computational effort. Extensive computational experiments on a set of realistic instances from the industry show that high productivity of the cutting equipment can be obtained with a minimal increase in the total area of used boards. The experiments also show that the proposed algorithms perform extremely well when compared with four commercial software tools available for the solution of the problem.