Cost minimization through optimized raw material quality composition

Lumber, a heterogeneous, anisotropic material produced from sawing logs, contains a varying number of randomly dispersed, unusable areas (defects) distributed over each boards' surface area. Each board's quality is determined by the frequency and distribution of these defects and the board's dimension. Typically, the industry classifies lumber into five quality classes, ranking board quality in respect to use for the production of wooden components and its resulting material yield. Price differentials between individual lumber quality classes vary over time driven by market forces. Manufacturers using hardwood lumber can minimize their production costs by proper selection of the minimum cost lumber quality combination, an optimization problem referred to as the least-cost lumber grade-mix problem in industry parlance. However, finding the minimum cost lumber quality combination requires that lumber cut-up simulations are conducted and statistical calculations are performed. While the lumber cut-up simulation can be done on a local computing workstation, the statistical calculations require a remote station running commercial statistical software. A second order polynomial model is presented for finding the least-cost lumber grade-mix that manufacturers of wood products can use to minimize their raw material costs. Tests of the newly developed model, which has been incorporated into a user-friendly decision support system, revealed that only a limited amount of lower quality raw material (e.g. lumber with a high frequency of defects in boards and/or small board sizes) can be accepted, as otherwise the lumber quality mix cannot supply all the parts required. However, the new model suggested solutions that resulted in lower raw material costs than solutions from older models.