Combining a decomposition strategy with dynamic programming to solve spatially constrained forest management scheduling problems

Abstract

A decomposition approach to solve the forest management scheduling adjacency problem is developed for application to large forests. Overlapping subproblems amenable to exact dynamic programming solution are solved sequentially. A heuristic is used to define and link subproblems such that near-optimal solutions to the master problem are obtained. Both the contrasting size and the irregular shape of stands complicate the problem of formulating the dynamic programming network. Subproblem size and the sequencing of stands for each corresponding dynamic programming network are defined simultaneously, as model size is especially sensitive to stand sequencing. Emphasis is on efficient dynamic programming formulations to allow for large subproblems. Results from over 100 test computer runs are discussed for applications to 3 large problems. Results suggest that the strategy can consistently produce near-optimal solutions at reasonable computational cost. A procedure is developed to derive three slightly different adjacency problems so that the optimal solution can be found. Results for applications to the modified problems show that the proposed heuristic's solutions were within 0.01, 0.04, and 0.01% of the optimal solution, respectively. The proposed solution method consistently outperformed two other heuristics that were applied.