Log Bucking and Lumber Manufacturing Using Dynamic Programming

The process of converting a tree into finished lumber involves several interrelated steps. The two of greatest potential for improvement are cutting the felled tree into shorter logs (called bucking the tree) and sawing the bucked logs into lumber. Unlike previous work in the area, this paper considers the two activities together as a single production system. The model allows for variations in tree shape and quality which could be recorded by modern electronic scanners. Among the principal techniques used in the paper are dynamic programming for both bucking and sawing, and a procedure for calculating the distance between two polyhedral sets in R². Computational experience is reported on trees with representative defect patterns, taper, and sweep.