A dynamic programming approach to optimizing stem conversion
The process of converting trees into roundwood logs is the first in a series of manufacturing steps that ultimately leads to a finished product such as plywood, lumber, or paper. Since each manufacturing step is dependent on previous actions, potential profits can be lost if trees are miscut. The decision problem facing the log bucker is complicated by the shape and quality characteristics of the tree, the log scaling and grading practices that must be applied, the variety of log size specifications, the alternative end uses, end product recovery, and the economic framework.This study develops a dynamic programming model for finding the optimum solution for bucking individual trees. The model considers shape characteristics of the tree such as taper, sweep, and crooks and utilizes descriptions of external and internal defects in considering log scaling and grading practices. A flexible framework allows management to indicate log specifications and economic factors appropriate to a particular analytical setting. The optimum solution which maximizes the conversion surplus of logs in the tree can be found for cases where logs are produced for sale on a roundwood log market or when a firm produces logs for its own processing facilities. In this latter case, provision is made to utilize predictions of end product and residue recovery in assessing conversion surplus.An analysis of five old growth Douglas-fir trees demonstrated the effect of considering defects and end product information. The mix of logs in optimal solutions with and without this information is very different. This has implications for those attempting to use computer based automatic bucking systems which may not have the capability to access and utilize information on all factors pertinent to bucking decisions.The model will be useful as a tool in training bucking crews, in providing a benchmark for evaluating bucking policies, and may become feasible in conjunction with appropriate scanning and computing technologies in optimizing and automating log bucking stations and log merchandisers. Extension of dynamic programming to other areas of manufacturing such as veneer clipping and lumber edging and trimming appears to be straightforward.
- Forestry