The Influence of Cutting-Bill Requirements on Lumber Yield Using a Fractional-Factorial Design Part I. Linearity and Least Squares
Keywords:Cutting-bill requirements, lumber yield, rip-first rough mill, fractional-factorial design, interaction between cutting-bill requirements and yield, influence of part size and quantity on yield
The importance of lumber yield on the financial success of secondary solid wood products manufacturers has been known for quite some time. Various efforts have been undertaken to improve yield, such as inclusion of character marks (defects) in parts, "cookie-cutting" of boards, improved optimization algorithms, or improved cut-up technologies. For a variety of reasons, the relationship between cutting-bill requirements and lumber yield has attracted limited attention. This is Part I of a 2-part examination of this relationship.
The standardized and simplified Buehlmann cutting bill and the Forest Service's Romi-Rip lumber cut-up simulator were used in this study. An orthogonal, 220-11 fractional-factorial design of resolution V was used to determine the influence of different part sizes on lumber yield. All 20 part sizes contained in the cutting bill and 113 of a total of 190 unique secondary interactions were found to be significant variables in explaining the variability in observed yield. Parameter estimates for the part sizes and the secondary interactions were used to specify the average yield contribution of each variable. Parts 445 mm long and 64 mm wide were found to have the most positive influence on yield. Parts smaller than 445 by 64 mm (such as, for example 254 by 64 mm) had a less pronounced positive yield effect because their quantity requirement is relatively small in an average cutting bill. Thus, the quantity required is obtained quickly during the cut-up process. Parts with size 1842 by 108 mm, on the other hand, had the most negative influence on high yield. However, as further analysis showed, not only the individual parts required by a cutting bill, but also their interaction determines yield. In general, it was found that by adding a sufficiently large number of smaller parts to a cutting bill that required large parts, high levels of yield can be achieved.
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