Optimizing the management of uneven-aged forest stands: A stochastic approach

Mathematical programs used for management and policy decisions in natural resources normally contain at least one underlying component which is stochastic. A technique is presented that allows marginal, conditional, and empirical confidence regions to be calculated for a widely known model of optimal uneven-aged stand structure. The technique uses the nonparametric bootstrap to approximate the joint sampling distribution for the decision variables of the nonlinear programming model. Subsequently, multivariate normal theory is used to obtain 95% confidence statements on the decision variables and functions thereof. Results show that the optimal steady-state investment-efficient diameter distribution for uneven-aged northern hardwood stands is an imprecise estimate given the data used for growth model calibration and the assumptions of the mathematical model. However, confidence statements found using this methodology are only approximate as they rely on an estimate of the sampling distribution for the optimal diameter distribution, not on classical statistical theory. These findings suggest a very real need for modelers, managers, and policy makers to begin considering the role of stochastic model components in mathematical programming models in natural resources.