Optimal control and parameter selection problems in forest stand management

A typical stand forestry problem for determining an optimal silvicultural regime is demonstrated in this paper, where an optimal number of trees at planting and a harvesting strategy over the crop rotation are resolved. The traditional approach for determining such strategies is to formulate a dynamic programming problem where the stages and decision variables are pre-determined in a forward recurrent procedure and thus eliminating any possibilities of an exhaustive search. This type of formulation is largely driven by the 'curse of dimensionality'. Our formulation is a combined optimal control and parameter selection problem using Pontryagin's maximum principle where, the optimal control part determines the harvesting strategy, and the parameter selection determines the initial number of trees planted. Dynamical models are developed as the building blocks of the optimal control and parameter selection formulation using Eucalyptus nitens data froze intensively managed stands, courtesy of North Forests Products, Tasmania, Australia.