published_or_final_version / Mathematics / Master / Master of Philosophy

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The main goal is to develop decision policies for individual forest stand management. It addresses three major areas of interest in the optimal management of individual forest stands: incorporating a two-species growth and yield model into a single stand management model, incorporating a comprehensive list of management options into a single stand management model, and incorporating uncertainty into a single stand management model. Dynamic programming (DP) is a natural framework to study forest management with uncertainty. The forest stand management problem, as modelled in this thesis, has a large dimensional state space with a mix of discrete and continuous state variables. The DP model used to study this problem is solved by value iteration with the objective of understanding infinite horizon policies. However, since some of the state variables are continuous, all states can’t be examined in an attempt to create the cost-to-go function. Therefore, the cost-to-go function value is calculated at a given stage of the algorithm at a finite set of state points and then the cost-to-go values are approximated on the continuous portion of the state space using a continuous function. All of this is done with random processes impacting state transitions. With the mixed-species growth model developed in this thesis, a comprehensive list of management options can be incorporated into the DP model and, with the addition of uncertainty from sources such as market prices and natural disasters, near optimal stand management policies are developed. Solving the DP model with the required level of detail lead to the development of insight into function fitting on continuous state spaces and to the development of cost-to-go function approximation bounds. Studying the policies shows that the addition of uncertainty to the model captures the dynamics between market prices and stand definitions, and leads to policies that are better suited to decision making in a stochastic environment, when compared with policies that are developed with a deterministic model. Enough precision is built into the DP model to give answers to typical questions forest managers would ask.

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