Derivation of optimal stocking policies for grazing in arid regions. I. methodology

摘要

The extensive nature of grazing in arid areas requires that the derivation of optimal stocking policies be conducted at paddock level, if management of the grazing process (including constraints to prevent deterioration of the vegetation and soil resources) is to be represented realistically. Although stochastic linear and dynamic programming provide equivalent, satisfactory representations of the stochastic nature of this process, stochastic dynamic programming is more suited to the derivation of optimal stocking policies for arid areas, for several reasons. The simple stochastic dynamic-programming model of grazing developed in this paper demostrates the power of the procedure and the nature of the optimal stocking policy. It is novel in that both the economic objective function and the state equations are nonlinear functions of the stochastic state variables. Prices of sheep and wool may also be included as stochastic variables, and probabilistic constraints on minimum levels of vegetation density can be implemented straightforwardly. Estimation of realistic joint probability density functions of state transitions during each decision period is a necessary but difficult task in any stochastic optimization procedure. The use of simulation experiments specifically designed for this purpose is seen as a solution, as well as being a means of incorporating the effects of many variables which cannot be included as state variables in the stochastic optimization procedure.