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

Abstract

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.

Special issue on: Computational discrete optimization

“…-Cutting and sequence optimization problems arise in many industrial applications, but are often computationally hard to solve. Ackermann and Diessel (2020) consider an integrated packing and sequence-optimization problem arising in the production of glued laminated timber in sawmills, where wood beams of different height and length shall be packed into a sequence of pressing steps subject to certain packing constraints of the press and requirements on subsequent pressing steps. They develop a heuristic three-stage solution approach for this problem and demonstrate its computational efficiency in a comprehensive numerical study using realistic input data.…”