Predicting Terminal Time And Final Crop Number For A Forest Plantation Stand:Pontryagin's Maximum Principle

Abstract

A lot of work has gone into developing management strategies for forest plantation stands. Analysts have resorted to the use of dynamic programming to find an optimum management strategy for a stand. The sterile 'curse of dimensionality' in dynamic programming computations has lead to the pursuit of alternative heuristic search algorithms that are plagued with the inherent inability to verify optimality. Optimality in stand management has always been a lingering issue in forest literature, since stand optimisation formulations started appearing in forest science journals from the early 1960s. Pontryagin's Maximum Principle was long cited as a potential exact solution technique, but there was never a demonstration of this technique with stand measurement data. However, using dynamical models as building blocks and based on stand measurement data, the authors have demonstrated the applicability of Pontryagin's Maximum Principle, avoiding the curse of dimensionality. All formulations demonstrated so far have not addressed the terminal time and constraint problem. What is presented in this paper is a combined optimal control and parameter selection formulation, using Pontryagin's Maximum Principle. The parameters are the initial planting density and final crop number where the optimal control is the harvesting strategy, all estimated for a specific rotation length.