Comparing adjacency constraint formulations for randomly generated forest planning problems with four age-class distributions

Three types of adjacency constraint formulations – pairwise, Type I ND (nondominated), and NOAM (new ordinary adjacency matrix) – were compared on 900 hypothetical, randomly generated, spatially explicit forest management problems with between 50 and 350 stands. Forests were generated using four age-class distributions, nominally called immature, regulated, overmature, and old-growth. Management planning problems with adjacency constraints were formulated for these forests in Model 1 format based on a planning horizon consisting of three 20 yr periods. The problems also included flow constraints and minimum average age requirements for the ending forest. For all age-class distributions, the Type I ND constraint type resulted in significantly lower solution times than either the Pairwise or the NOAM constraint types. NOAM constraints performed better than Pairwise constraints for immature forest problems, but Pairwise constraints performed better than NOAM constraints for overmature and old-growth forest problems. There was no difference between these two constraint types for regulated forest problems. Results also show that the age-class distribution of the forest is one of the most important factors determining the time needed to solve forest management problems with adjacency constraints. In general, the more mature the forest, the harder the problem is to solve. In particular, problems based on the old-growth age-class distribution typically took much longer to solve than comparable problems based on the other age-class distributions.