Constructing and selecting adjacency constraints

Maintaining spatial integrity is an important concern in both the tactical and operational levels of forestry planning. Spatial relationships are typically represented by adjacency constraints. The number of needed adjacency constraints for even a small number of planning units, if not kept to a minimum, may be too large to include in a mathematical programming formulation. Several approaches have been developed to ‘minimize’ the number of adjacency constraints used. These approaches involve either constraint subset selection or constraint aggregation. The authors demonstrate that with constraint aggregation the theoretical minimum of necessary adjacency constraints is one. However, the range of coefficients of one aggregated adjacency constraint is impractical for actual application. As an alternative, the authors explore the approach of identifying a minimal subset of a class of structural adjacency constraints. As a part of this approach, they develop a two-stage procedure to identify and fine tune a minimal subset of constraints for representing adjacency conditions so that there is no loss of spatial detail. Concise mathematical formulations are presented for each stage. This process is easy to implement and yields a relatively small number of ‘tight’ adjacency constraints.