An application of deterministic and robust optimization in the wood cutting industry

In the veneer cutting industry tree trunks are peeled into thin veneer strips which are cut, glued together, and pressed into bentwood pieces for seats, backrests, etc. In this work, a model for optimizing the inherent cutting problem with respect to resource efficiency is presented. Especially the heterogeneous quality of the wood renders existing models for classic cutting stock problems useless and calls for a new modeling approach. By means of the model presented in this paper, the problem is solved to optimality for real-world instances in reasonable time and applicable solutions are generated. Furthermore, in order to deal with uncertainties in the wood quality, the approach of robust optimization is applied to the problem. Robust optimization is an important tool to deal with uncertainties in the formulation of mathematical optimization models. Different concepts of robustness have been provided in the literature, one of which is the concept of minmax robust efficiency for uncertain multi-objective optimization problems. The concept of minmax robust efficiency is applied to a simplified version of the problem, robust efficient solutions are calculated, and the paper concludes with the discussion of the benefit of these solutions.