An optimization approach for sustainable development planning of savanna systems

A savanna system is a natural ecosystem in which the competition between grass and woody vegetation in a semi-arid rangeland should be maintained for its sustainable development. Finding an optimal management plan for obtaining maximum economic profit from raising cattle without loss of sustainability of the savanna system during a planning period is a great challenge for rangeland managers. In this study, we formulate the sustainable development planning of the savanna system as an optimal control model, in which maximization of the stocking rate of cattle during the planning period is chosen as the objective while sustainable development requirements are achieved through the constraints represented by the desired final state of the system. Using Pontryagin's maximum principle, the model is transformed into a two-point boundary-value problem with nonlinear differential equations that is then solved using an iterative approach. An example with a specified desired final state in a savanna system without fire is used to demonstrate the performance of the model and the algorithm. Numerical experiments show that the planning strategy obtained from the optimal control model achieves maximum economic profit from raising cattle during the planning period and simultaneously improves the resilience of the system and maintains sustainable development of the rangeland. The outcomes demonstrate that resilience, sustainable development and economic profit are consistent concepts in optimal management strategy for rangeland management.