Temporal and spatial harvesting of irregular systems of parcels

Spatial management issues have assumed a central position in planning for forest ecosystems in the United States on both public and private lands. The arrangement of management activities, especially harvesting activities, can often have adverse impacts on other neighboring areas of the forest. Thus, spatially explicit programming models, which can account for or prevent certain arrangements of activities or land allocations through the use of harvest adjacency constraints, have received considerable attention in the literature. The need for spatial specificity in programming models has led to the development of integer programming or mixed integer programming models. Given that integer programming problems are often viewed as a difficult class of problems to solve, heuristic solution methods have most often been used to solve spatially constrained forest management models. In this paper, a discrete (0–1) integer programming model that maximizes harvested timber volume over a multiperiod time horizon subject to harvest adjacency constraints is developed and tested for irregular, realistic systems of parcels. This model performed well computationally for many example configurations and was solved exactly using the simplex algorithm and limited branching and bounding. Certain spatial configurations with long time horizons did, however, require a nontrivial amount of branching and bounding. The model was tested using both contrived and real spatial data sets.