Forest ecosystem management often requires spatially explicit planning because the spatial arrangement of harvests has become a critical economic and environmental concern. Recent research on exact methods has addressed both the design and the solution of forest management problems with constraints on the clearcut size, but where simultaneously harvesting two adjacent stands in the same period does not necessarily exceed the maximum opening size. Two main integer programming approaches have been proposed for this area restriction model. However, both encompass an exponential number of variables or constraints. In this work, we present a new integer programming model with a polynomial number of variables and constraints. Branch and bound is used to solve it. The model was tested with both real and hypothetical forests ranging from 45 to 1,363 polygons. Results show that the proposed model's solutions were within or slightly above 1% of the optimal solution and were obtained in a short computation time.

Green-up requirements are of great interest for forests near cities since these forests are commonly used for recreational activities by the local population as well as for commercial forestry activities. We present three formulations to establish green-up requirements, based on a dynamic green-up approach and constructed by means of: (i) a predefined fixed length for the green-up time, (ii) a predefined variable length for the green-up time and (iii) height information produced by the growth simulator. Additionally, restrictions on harvested volume and maximum open areas were applied. All the green-up formulations were applied to five datasets comprising different initial forest conditions regarding age and site index distribution. Results show that higher net present values are obtained by the formulation that allow a predefined variable length for the green-up time and by using the height information from the growth simulator compared to the formulations using a predefined fixed length for the green-up time. The increase in NPV was most pronounced for the old forest datasets and varied between 4.23% and 8.15%. The optimal solution was always found when modeling the green-up requirement using the height information. This formulation also tended to find optimal solutions faster than other formulations.