Inter-Temporal Aggregation for Spatially Explicit Optimal Harvest Scheduling under Area Restrictions

Abstract

Abstract 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.