Adjacency Branches Used to Optimize Forest Harvesting Subject to Area Restrictions on Clearfell

Abstract

Consider a forest containing units of various sizes for which a maximum clearfell area has been specified along with an associated green-up time period. For such an application it is customary to use adjacency constraints to produce a harvesting plan. These constraints control the availability for harvest of specific units relative to the harvesting of certain adjacent units. However, such constraints are difficult to formulate and often precipitate major difficulties in the implementation of the solution algorithm. A new concept, a nuclear set, is introduced. This concept allows the unit-specific aspects of the problem to be analyzed in an insightful manner. Any adjacency violation can be detected in relation to these nuclear sets. Suitable adjacency branches can be implemented to remove these violations. The form of these branches derives from the same nuclear sets. A remarkably small number of these branches are required to obtain a feasible solution. These ideas are incorporated into a column generation and constraint generation model. This new forest harvesting model solves the clearfell area restriction problem in an exact sense. Results are included for numerical trials involving simulated data representing moderately sized applications with a planning horizon of up to one rotation. The output from these trials suggests that this algorithm is suitable for large commercial applications. Several applications of 1,600 units are solved over 25 time periods with multiple green-up.