Choosing Prices to Optimally Buck Hardwood Logs with Multiple Log-Length Demand Restrictions

Abstract

Abstract The purpose of this article is to present a hierarchical optimization approach that selects prices which, when used in a single stem bucking optimization model, produce a specified mix of logs by grade and length. The model is developed to address the demand constrained optimal bucking situation for northern hardwoods. The demand constraints are minimum percentages needed in four log lengths [3.0 m (10 ft), 3.7 m (12 ft), 4.3 m (14 ft), and 4.9 m (16 ft)] to meet order requirements from veneer buyers. There are two levels in the hierarchical optimization system: at the lower level, a dynamic programming model is used to optimize the value of each individual tree, while the upper level is a linear programming model which finds one or more sets of prices, each used some portion of the time, that produce the required product mix in the lower level model. The hierarchical model is solved iteratively until a single set of prices satisfies all demand constraints. This approach is distinctly different than traditional approaches, which pass different information between the upper and lower level models to solve two-level optimization problems. The parameters passed in traditional approaches are shadow prices in one direction and production levels in the reverse direction. The model developed could be adapted to other species and log grading rules whenever several competing demand constraints exist. Furthermore, the approach could be adapted to a wide range of hierarchical planning applications where inputs, and therefore the production possibilities curve, are fixed and constraints apply. For. Sci. 43(3):403-413.