Spatially explicit forest harvest scheduling with difference equations

Spatially explicit harvest scheduling models optimize the layout of harvest treatments to best meet management objectives such as revenue maximization subject to a variety of economic and environmental constraints. A few exceptions aside, the mixed-integer programming core of every exact model in the literature requires one decision variable for every applicable prescription for a management unit. The only alternative to this “brute-force” method has been a network approach that tracks the management pathways of each unit over time via four sets of binary variables. Named after their linear programming-based aspatial predecessors, Models I and II, along with Model III, which has no spatial implementation, each of these models rely on static volume and revenue coefficients that must be calculated pre-optimization. We propose a fundamentally different approach that defines stand volumes and revenues as variables and uses difference equations and Boolean algebra to transition forest units from one planning period to the next. We show via three sets of computational experiments that the new model is a computationally promising alternative to Models I and II.