Investigating the Linearity Assumption Between Lumber Grade Mix and Yield Using Design of Experiments (DOE)

Xiaoqiu Zuo, Urs Buehlmann, R. Edward Thomas


Solving the least-cost lumber grade mix problem allows dimension mills to minimize the cost of dimension part production. This problem, due to its economic importance, has attracted much attention from researchers and industry in the past. Most solutions used linear programming models and assumed that a simple linear relationship existed between lumber grade mix and yield. However, this assumption has never been verified or rejected with scientific evidence. The objective of this study was to examine whether a linear relationship exists between yield and two- and three-grade lumber combinations using the USDA Forest Service's ROMI-RIP rough mill simulator and a cutting bill created by Buehlmann. The results showed that a simple linear relationship between grade mix and yield exists only for some grade combinations, but not for others. These findings were confirmed by repeating the tests using actual cutting bills from industry. It was observed that cutting bill characteristics, especially part length requirements and the lumber grades involved, are influential in causing a simple linear or nonlinear relationship between grade mix and yield.


Lumber grade mix;least-cost lumber grade mix;simple linearity;mixture design

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