This study proposes a discrete optimal control model to obtain harvest strategies that maximize the net present value (NPV) of the timber harvested from uneven-aged Pinus nigra stands located in the Spanish Iberian System, between two stable positions. The model was constructed using an objective function that integrates financial data on the harvesting operations with a matrix model describing the population dynamics. The initial and final states are given by the stable diameter distribution of the stand, and the planning horizon is 70 years. The scenario analysis corresponding to the optimal solutions revealed that the stand diameter distribution does not deviate substantially from the equilibrium position over time and that the NPV for the optimal harvesting schedule was always greater than the NPV for the “sustainable/stable” harvesting strategy. The NPV increase for the different scenarios is between 5.36% and 14.43%, showing a greater increase in higher site index scenarios and higher recruitments.

Traditional uneven-aged forest management seeks a balance between equilibrium stand structure and economic profitability, which often leads to harvesting strategies concentrated in the larger diameter classes. The sustainability (i.e., population persistence over time) and influence of such economically optimal strategies on the equilibrium position of a stand (given by the stable diameter distribution) have not been sufficiently investigated in prior forest literature. This article therefore proposes a discrete optimal control model to analyze the sustainability and stability of the economically optimal harvesting strategies of uneven-aged Pinus nigra stands. For this model, we rely on an objective function that integrates financial data of harvesting operations with a projection matrix model that can describe the population dynamics. The model solution reveals the optimal management schedules for a wide variety of scenarios. To measure the distance between the stable diameter distribution and the economically optimal harvesting strategy distribution, the model uses Keyfitz’s delta, which returns high values for all the scenarios and, thus, suggests that those economically optimal harvesting strategies have an unstabilizing influence on the equilibrium positions. Moreover, the economically optimal harvesting strategies were unsustainable for all the scenarios.

This paper proposes a simple and direct method to provide reliable approximations of the net present value (NPV) and the perpetual value (PV) of sustainable timber harvests from a monospecific uneven-aged forest based on dimensionless numbers. In addition, two new dimensionless numbers ρNPV and ρPV are introduced. These use the NPV or PV derived from the sale of timber throughout a harvest cycle, plus the final stocking value (as numerator), and the fair value of standing timber under IAS 41 (as denominator). They can be interpreted as economic performance indicators for forest management, inspired by the return on assets accounting concept, showing how profitable the forest is, relative to its total value, with sustainability and stability criteria. Those approximations to the variables NPV, PV, ρNPV and ρPV, were obtained under conditions of stable equilibrium from a matrix model. In order to exemplify and test the results, the model used data from uneven-aged managed Pinus nigra stands, considering three levels of tree diameter growth, six levels of basal area and 33 levels of recruitment, creating a total of 594 planning scenarios. Furthermore, the study revealed the existence of strong linear correlations between those variables and a dimensionless number.