Tactical and strategic planning for rangeland resource use : an optimal control approach

Abstract

This inquiry addresses the need for a grazing optimization framework to include nonstationary effects of grazing due to over or under utilization (with respect to a steady state stocking rate of 9 acres./amu). The mechanism is based upon a continuous-time control approach whose (differential) equation of motion reflects both natural and induced changes in forage level with respect to time. The methodology provides an interface between tactical and strategic decisions regarding stocking rate. The study area is the Texas Experimental Ranch at Throckmorton, located in the eastern half of the Texas Rolling Plains. The entire set of biological factors is range cite-specific to that region. The objective function is the (statistical) expectation with respect to forage level of the integral of net returns to land, management, and capital through time, where initial time is 0 and final time is 10 years. Evaluation for solution occurs daily. The stocking rate path (control variable) that maximizes the objective function is selected. The state is actually a random variable-forage level. It is shown that forage level through time is well described as a Wiener process. A terminal constraint on forage level is introduced which then requires the interchange of order of integration and using the expected forage level everywhere instead of forage level. Furthermore forage demand and a nonlinear time continuous cow-calf-cottonseed meal price system was estimated. Several runs were made with alternative shifts and combinations of shifts in output price level (cow and calf), feed price level, interest rate and terminal level of forage. The objective function was sensitive to output prices, input prices, and interest rate. The optimal stocking rate path however was not as sensitive. Unless output prices became very high and/or input prices became extremely low, the optimal stocking rate path remained at 11 acres./amu. At this level, there was some feeding since the ratio of forage supply to demand fell below a critical value, but the duration of the supplemental feeding was only about one month...