Incorporating aspects of habitat fragmentation into long-term forest planning using mixed integer programming

In forest planning, an understanding of the spatial relationships between compartments has become an increasingly important issue. Effective approaches must, therefore, be developed that include consideration of spatial relationships in planning models. Existing approaches, based on numerical optimization, tend to lack the means effectively to include spatial considerations. Further, many suggested approaches have focused on ways to include adjacency constraints or green-up constraints in forest planning. However, in order to maintain the biodiversity in the forest, methods dealing with, for instance, the problem of fragmentation of old forests, also have to be developed. In this paper, the issue of fragmentation is addressed and incorporated into long-term forest planning. The approach is to attempt to minimize the outer perimeter of areas of old forest. The model presented is formulated on the basis of mixed integer programming, and solved with a branch and bound algorithm. A data set consisting of 924 stands was used to examine the model, which was then evaluated with different requirements for the degree of clustering. The results indicate that the model is effective for the clustering of old forest stands and that it can be solved within a reasonable time despite the large number of constraints and variables. In the case study the loss in net present value as a result of including the issue of fragmentation was a few percent.