Linear programming and optimizing lumber quality composition in secondary hardwood dimension mills

Abstract

Linear programming has been widely applied in the secondary hardwood dimension manufacturing industries to solve the least-cost lumber grade mix problem, which refers to the search for minimal raw material costs. Most existing models are based on the assumption of a simple linear relationship between lumber grade mix and yield. However, this crucial assumption has never been veri®ed.In this study, the results from a ®ve-factor mixture design statistically proved that none of the cutting bills tested has a simple linear relationship between yield and di erent lumber grade mixes. It was observed that cutting bill characteristics and lumber quality a ect the relationship between yield and lumber grades. Cutting bills that require wider and/or longer parts tend to behave non-linearly. In addition, the more dissimilar lumber grade qualities that are processed, the more likely is the occurrence of a non-linear response.The inability to predict the relationship between yield and lumber grades, coupled with the high percentage of non-simple linear relationships observed in this study, brings into question the validity of the linearity assumption applied in previous linear programming models. Further e orts are needed to construct a new least-cost lumber grade mix model that does not rely on the assumption of a simple linear relationship between lumber grade mix and yield.