Managing cattle grazing under degraded forests: An optimal control approach

In this paper aspects of knowledge generation and administration concerning management of a rural enterprise in the Argentine Chaco region are analyzed. The deterioration of natural resources and human living conditions show that forest–cattle interaction and the ecological economics of the system are poorly understood or not properly taken into account. A methodological solution to a typical decision-making problem is proposed here and illustrated by a worked example extracted from a real feasibility study. The introduction provides a summary of the natural history and of the human interventions in the region. Arguments on the role of silvopastoral systems in reverting forest and soil degradation into sustainable productive undertakings are also exposed. The mathematical treatment of the problem follows a system theoretic approach. A basic nonlinear model for the dynamics is designed first. Its simplest version includes three state variables (livestock units, forest biomass and forage availability) and two manipulated variables (percentage of female calves sold each year and percentage of the cows that did not give birth during the past period and went for sale). States and controls are related by coupled differential-difference equations. Selected results from simulation are shown. Foundations are also laid for taking into account impulsional controls (selective and massive wood extractions, forage implantation, cattle additions and sales). The objective function reflects sustainable development principles. It evaluates the process in terms of usual economics and introduces ecological components of the management strategy. The total cost is expressed as the accumulation of net expenses made for a fixed number of years, minus the sale value of the firm at the end. Then a dynamic programming scheme is developed for finding optimal trajectories with respect to the basic setup. Shadow prices for the states are derived from the solution. Progress towards the building of a decision support system with the preceding elements is reported.