Branch-and-cut for the forest harvest scheduling subject to clearcut and core area constraints

Integrating forest fragmentation into forest harvest scheduling problems adds substantial complexity to the models and solution techniques. Forest fragmentation leads to shrinking of the core habitat area and to weakening of the inter-habitat connections. In this work, we study forest harvest scheduling problems with constraints on the clearcut area and constraints on the core area. We propose a mixed integer programming formulation where constraints on the clearcut area are the so-called cover constraints while constraints on the core area are new in the literature as far as we know. As the number of constraints can be exponentially large, the model is solved by branch-and-cut, where the spatial constraints are generated only as necessary or not before they are needed. Branch-and-cut was tested on real and hypothetical forest data sets ranging from 45 to 1363 stands and temporal horizons ranging from three to seven periods were employed. Results show that the solutions obtained by the proposed approach are within or slightly above 1% of the optimal solution within three hours at the most.