A hierarchical approach for solving an integrated packing and sequence-optimization problem in production of glued laminated timber

Integrated packing and sequence-optimization problems appear in many industrial applications. As an example of this type of problem, we consider the production of glued laminated timber (glulam) in sawmills: Wood beams must be packed into a sequence of pressing steps subject to packing constraints of the press and subject to sequencing constraints. In this paper, we present a three-stage approach for solving this hard optimization problem: Firstly, we identify alternative packings for small parts of an instance. Secondly, we choose an optimal subset of these packings by solving a set cover problem. Finally, we apply a sequencing algorithm in order to find an optimal order of the selected subsequences. For every level of the hierarchy, we present tailored algorithms, analyze their performance and illustrate the efficiency of the overall approach by a comprehensive numerical study.