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Seeking an optimal operational regime under different management environments has been one of the main concerns of forest managers. Traditionally, the main operational regime includes planting density or regeneration scheme, thinning time/intensity, and optimal time to harvest over the given time horizon. Deterministic approaches to tackle this type of optimization problem with different controls have dominated the solution techniques in forestry literature. We present in this paper an overview of the methodologies used in stand-level optimization, in which we show the strengths and weaknesses of these methodologies as well as provide comments on the effectiveness of the methodology. We then propose a new dynamic programing approach for generalizing solution specification and techniques.

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The choice of a baseline against which to evaluate changes in carbon stocks is a critical component of any forest carbon offset market. In this paper, we use a discrete dynamic programming model and data from a lodgepole pine (Pinus contorta Douglas ex Loudon) stand in northeastern British Columbia, Canada, to demonstrate that different baselines have little or no effect on optimal harvest decision but can have a large impact on economic returns to a landowner. The results reveal that the magnitude of the financial return to the landowner is dependent on the starting conditions of both the predetermined baseline and the proposed carbon offset project. The study also shows that when given the choice between alternative baselines, a landowner will always choose a fixed baseline over a business-as-usual baseline.

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We propose a new approach to solve inter-temporal unit aggregation issues under maximum opening size requirements using two models. The first model is based on Model I formulation with static harvest treatments for harvest activities. This model identifies periodic harvest activities using a set of constraints for inter-temporal aggregation. The second model is based on Model II formulation, which uses dynamic harvest treatments and incorporates periodic harvest activities directly into the model formulation. The proposed approach contributes to the literature on spatially constrained harvest scheduling problems as it allows a pattern of unit aggregation to change across multiple harvests over time, as inter-temporal aggregation under a maximum opening size requirement over period-specific duration. The main idea of the proposed approach for inter-temporal aggregation is to use a multiple layer scheme for a set of spatial constraints, which is adapted from a maximum flow specification in a spatial forest unit network and a sequential triangle connection to create fully connected feasible clusters. By dividing the planning horizon into period-specific durations for different spatial aggregation patterns, the models can complete inter-temporal spatial aggregation over the planning horizon under a maximum opening size requirement per duration. Study Implications Inter-temporal unit aggregation is important because it provides flexible aggregation patterns for maximum opening size problems with multiple harvests over time. We have proposed a new modeling approach capable of solving spatially constrained harvest scheduling problems by allowing a pattern of unit aggregation to change across multiple harvest periods over time, as inter-temporal aggregation under flexible maximum opening size requirements. Forest managers can benefit from this approach for their future requirements based on the public interests as well as their own.