Dynamic programming for optimization of timber production and grazing in ponderosa pine

Abstract

Dynamic programming procedures are presented for optimizing thinning and rota- tion 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 discussed. FOREST SCl. 28:517-526. THE APPLICATION OF DYNAMIC PROGRAMMING (DP) for the simultaneous deter- mination of thinning intensity and rotation has been discussed by Hann and Bro- die (1980). A typical DP formulation (e.g., Brodie and Kao 1979) maximizes the cumulative net present value of timber harvested over discrete levels of each of several state descriptors at each time stage defined in the network. Although DP formulations are becoming increasingly complex in terms of number of state descriptors and treatment options (e.g., Kao 1980), objective functions usually have been based on the value of timber only. In this paper, we demonstrate the use of dynamic programming for the simultaneous determination of thinning in- tensity and rotation for ponderosa pine (Pinus ponderosa Laws.) when two out- puts, timber and forage, are considered in the objective function. Joint production is contrasted with production of each product independently, and the impact of changing relative values is discussed and demonstrated. Burde (1974) conducted a case study of timber and forage production for a hypothetical ponderosa pine forest in Arizona. He concluded that the forest should be managed under the concept of dominant use with commercial rangeland managed for forage production, commercial forest land managed for timber pro- duction, and lands submarginal for either purpose managed for yet other uses. The problem we address is that of determining the thinning regime that jointly maximizes the returns from both grazing and timber harvest on the same unit of