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Optimal Harvesting with Stand Density Targets: Managing Rocky Mountain Conifer Stands for Multiple Forest Outputs

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A solution is presented for the stand management problem of optimizing timber yields (expressed as either present value or volume production) while satisfying constraints intended to meet nontimber management objectives such as deer habitat or visual quality. The constraints are stand density targets formulated exogenously by the forest management staff and are expressed as a simple function relating both the minimum and maximum numbers of trees per acre to quadratic mean diameter. The goal is to find the sequence of diameter-class thinnings that maximizes yield while staying between the trees per acre bounds for each quadratic mean diameter. The solution method is a derivative-free coordinate-search process that incorporates penalty functions for the constraints. Examples focus on mixed-conifer stands in the Northern Rocky Mountains with three different land use designations: timber production, timber production in visually sensitive areas, and timber production in whitetailed deer winter habitat. Growth and yield is forecast dynamically with the Stand Prognosis Model. Results show that significant reductions in present value and volume production may result from meeting stand density targets. In addition, the solution algorithm quickly finds infeasible targets (all of the wildlife management constraints proved to be infeasible). Because the solution algorithm also provides near-feasible solutions, it is easy to identify specific targets that need to be relaxed to obtain feasibility. Thus, the results from the solution algorithm can be used to quantify the costs associated with meeting the nontimber management goals. Furthermore, results from such analyses should greatly assist in determining efficient levels of production for multiple forest outputs. For. Sci. 38(3):554-574.

Keywords: Multiple-use management; Stand Prognosis Model; constrained optimization; single-tree simulator

Document Type: Journal Article

Affiliations: Silviculturist, Northern Region, Box 7669, Missoula, MT 59807

Publication date: August 1, 1992

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