A Least-Cost Dynamic Optimization Approach for Obtaining a Desired Balanced Uneven-Aged Structure

There has been increasing interest among foresters and landowners in modifying existing even-aged forest structures to multi-aged or uneven-aged structures. Maintaining a continuous forest structure often provides a wider array of forest values over the long term. The conversion process is challenging in regions of the Northeast United States characterized by forests composed of dense diseased beech thickets and low-vigor deformed overstory trees. Abundance of noncommercial beech may result in negative cash flows during the conversion process to achieve a desired balanced uneven-aged structure. The Forest Vegetation Simulator was used to model growth and yield. Given the possibility of negative cash flows, a least-cost dynamic program with a penalty function was used to determine least-cost time paths for two management scenarios, one characterized by the successful removal of beech and the other simulating the continued presence of beech. Incorporating a penalty function allowed creating a continuum of least-cost paths from a zero penalty with the greatest weight given to net revenue goals to the largest penalty with the greatest weight given to ecological goals. Sensitivity analyses revealed least-cost paths were more stable given changes in prices and wages when greater emphasis was placed on the ecological goals associated with the target structure. Study Implications: There has been increasing interest in modifying existing even-aged forest structures to multi-aged or uneven-aged structures. However, in cases where the initial forest is dominated by undesirable growing stocks and might not provide sufficient revenue to cover management costs, a least-cost optimization would be more a suitable approach. The proposed method creates a continuum of least-cost paths from a zero penalty with the greatest weight given to net revenue goals to the largest penalty with the greatest weight given to ecological goals. This also allows identifying the opportunity cost of choosing one least-cost management regime over another. Finally, the landowner’s choice of the least-cost path most consistent with their management goals is the revealed optimal solution to maximize their welfare.