A Strengthening Procedure for the Path Formulation of the Area-Based Adjacency Problem in Harvest Scheduling Models

Spatially-explicit harvest scheduling models optimize the spatiotemporal layout of forest management actions to best meet management objectives such as profit maximization, even flow of products, or wildlife habitat preservation while satisfying a variety of constraints. This investigation focuses on modeling maximum harvest opening size restrictions whose role is to limit the size of contiguous clear cuts on a forested landscape. These restrictions, a.k.a. green-up constraints, allow adjacent forest stands to be cut within a pre-specified timeframe, called green-up period, only if their combined area does not exceed a limit. We present a strengthening procedure for one of the existing integer programming formulations of this so-called Area Restriction Model and test the computational performance of the new model on sixty hypothetical and seven real forest planning applications. The results suggest that the strengthened model can often outperform the other three existing formulations. We also find that the original Path Model is still competitive in terms of solution times.