“Stochastic and Multi-Criteria Models in Forest Planning”
Classical forest planning models consider multi-period decisions on harvesting and road building. These models are deterministic, considering expected values of relevant parameters and usually optimize net present value. In this talk we consider uncertainty, both in market prices, and also due to climate change, expressed as variability in tree growth. The uncertainty is expressed as scenarios, that is, a value for each relevant parameters (e.g. timber price) for each period through the horizon. We discuss how scenarios are generated, the resulting stochastic models where non anticipativity constraints must be added, and present decomposition approaches to solve large scale problems. We show the advantage in terms of quality of solutions obtained when uncertainty is considered explicitly in the planning models compared to the classic deterministic models. As an extension we analyze the case of risk averse decision makers, considering options such as value at risk and conditional value at risk. We also develop models for the case when, besides uncertainty, multiple objectives are considered besides economic value, such as carbon sequestration, land erosion, water quality. This can be handled searching for Pareto Optimal solutions or Goal Programming. We present computational solutions for realistic problems in each case.