Optimizing the Harvest Timing in Continuous Cover Forestry

Abstract

We analyze continuous cover or uneven-aged forest management with optimized harvest timing. The analysis is based on an economic description of uneven-aged forestry using a size-structured transition matrix model. In discrete time with fixed harvesting costs, optimizing harvest timing requires solving of a vector of integer variables in addition to the usual number of harvested trees. This mixed integer problem is solved using bilevel optimization, where the times of harvest are solved by a hill-climbing algorithm, and harvest intensities by a gradient-based interior point algorithm. Optimizing the integer harvest timing variables is crucial especially when the initial stand is an outcome of a plantation type of even-aged management and the forest owner prefers to continue forestry without clearcuts. Optimal harvest timing is shown to depend strongly on a fixed cost level, initial stand state, and interest rate. A steady state harvesting interval is typically 10–25 years, however, during transition it may be as long as 55 years. Increasing the interest rate decreases the average steady state capital value of the stand but may cause the steady state harvest frequency to decrease or increase due to flexibility in targeting harvests to different tree size classes. It appears that the legal limitations both in Sweden and Finland are constraining the optimal solutions.