Dynamic programming for optimization of timber production and grazing in ponderosa pine
Dynamic programming procedures are presented for optimizing thinning and rotation of even-aged ponderosa pine by using the four descriptors: age, basal area, number of trees, and time since thinning. Because both timber yield and grazing yield are functions of stand density, the two outputs-forage and timber-can both be optimized. The soil expectation values for single and joint production are derived and compared, and the impact of dynamic changes in relative price of the two products over the rotation is shown. Depending on relative prices and discount rate, the maximum soil expectations will be provided by timber alone, grazing alone, or an optimal schedule of joint production. Impacts of relative costs and values of the two outputs on management are discusses.