Application of Discrete-Time Optimal Control to Forest Management Problems

Abstract

Forests provide multiple ecosystem services, including woody and non-woody biomass products, contribution to carbon budget, and provision of public goods. Therefore, forest management problems are important in the context of optimizing those services. In this study, we formalize the spatial dynamic forest management model as the discrete-time optimal control problem with discrete time and age dynamics. The objective of the forest owner is to maximize the sum of discounted profits over time. Control variables stand for ratios of the forest harvested at every time period, every cell (forest type) and for each age class. In this setup, we deal with a high-dimensional bilinear control problem. The problem is solved using the discrete Pontryagin’s maximum principle. This approach allows us to derive an optimal solution in a constructive manner and reduce computational costs which may arise in the linear programming and recursive dynamics optimization methods. Results are illustrated by the model example with sample age-dependent cost functions, biomass factors, and price projection. Future research will deal with including mortality factors and disturbances into the model dynamics.