Optimizing the sequence of diameter distributions and selection harvests for uneven-aged stand management

The determination of an optimal sequence of diameter distributions and selection harvests for uneven-aged stand management is formulated as a discrete-time optimal-control problem with bounded control variables and free-terminal point. An efficient programming technique utilizing gradients provides solutions that are stable and interpretable on the basis of economic principles. Methods and results are demonstrated using a whole-stand/diameter-class simulator developed for northern hardwoods stands in Wisconsin. Examples in which the objective is present net worth maximization over a 150-year planning horizon with a 5-year cutting cycle suggest two types of optimal equilibrium stand structures: a downward-sloping diameter distribution if large value premiums are assigned to the largest diameter classes and a truncated diameter distribution if premiums for larger trees are gradual or absent. Transition strategies vary in length and harvest pattern depending on the stumpage value function used. It is emphasized that equilibrium management regimes developed with static analysis are not optimal when used as starting conditions in dynamic formulations.