A cutting stock problem in the wood products industry: a two-stage solution approach

In this study, a cutting stock problem is addressed to determine the width/length of the wooden boards and select lumber in standard lengths for cutting a cable spool. A nonlinear mathematical model is introduced using Pythagoras' theorem. The aim is to minimize the total length of lumber used and equivalently the total amount of wood wasted. To reduce the computational burden, the mathematical model is decomposed into two submodels for sizing and cutting decisions, and a two-stage decomposition algorithm is proposed for solving the submodels subsequently. A simulated annealing metaheuristic combining the first-fit decreasing and increasing techniques (SA-FFD/I) is proposed to show the computational efficiency of the decomposition approach. The savings on the total length of lumber used and the total amount of wood wasted in production are achieved by the decomposition algorithm, which is 8% and 86.4% on average compared to the SA-FFD/I heuristic. Accordingly, a numerical analysis is conducted on a real case to assess how capacity load and demand pattern scenarios impact the solution. The ratio between the total amount of wood waste and the total length of lumber does not exceed 2.54% for a weekly planning horizon.