Extending Harvest-Scheduling Using Spatial Optimization: Road Access and Edge Effects.

Abstract

The scheduling of management actions across forest stands is a fundamental task in the world of forestry. However, the spatial and temporal layout of management actions can lead to a combinatorial explosion of potential options to consider. Additionally, these management alternatives must often meet various constraints and limitations. The sheer quantity of options quickly pushes these problems out of the realm of “eyeballing” a good, or even feasible, solution. Because of this, managers have turned to optimization models to help determine the best harvest schedule that meets all requirements. Due to the computational complexity of these models, managers are forced to make simplifying assumptions, and to limit the scope of the models to only the most fundamental aspects. Now, with continued progress in both computational power and solution techniques, it is becoming both practical and feasible to extend these harvest scheduling models to consider broader aspects of the process. In this dissertation I consider two major extensions to harvest scheduling models: road access and edge effects. In chapter 1, I worked with the Washington State Department of Natural Resources to extend their harvest schedule modeling to consider the endogenous cost of rebuilding and maintaining the road network used to access a forest. I propose the Endogenous Fixed Charge Model (EFCM) to incorporate road costs that that vary endogenously with the system’s harvest decisions. In a case study in the Pacific Northwest, the EFCM was integrated into DNR’s standard workflows through the use of custom software called “Builder” that amended the EFCM constraints and variables to DNR’s exiting harvest schedule optimization. Results from the case study show the EFCM was able to increase net present value over a million dollars and to reduce the overall road network by some 14%. In chapter 2, I explore how edge effects between managed forest units can be controlled and mitigated. Newly created edges caused my management actions to alter the landscape and can affect many environmental factors. These altered environmental factors have a variety of impacts on forest growth and structure and can alter harvest yields and habitat for wildlife. After discussing how edge effects can arise from a variety of management actions, I propose a general optimization modeling framework to detect and flag newly created edges while determining an optimal management schedule. I use the real world context of clear-cut harvesting to illustrate multiple possible management objectives tied to the creation and delineation of newly formed edges. In a case study in the Pacific Northwest, I demonstrate how the modeling framework can be used to mitigate damage associated with increased wind exposure caused my neighboring harvests. Results from the case study show the modeling framework functions as intended and that a significant reduction in wind damage can be achieved by considering the spatial and temporal sequencing of harvest actions. In chapter 3, I return to the road access problem to examine how an alternative representation of the road network affects the solution behavior of a joint harvest-scheduling and road-access model using route-finding. Route-finding removes the assumption of predefined routes and allows the optimization model to choose the best hauling route while considering all other harvests that need routing. The number of constraints and variables used for route-finding depend on the size and configuration of the road network. Therefore it is important to consider how alternative representations of the road network effect the solution behavior of these difficult-to-solve models. To test network representations, I propose a Mixed Integer Program (MIP) to include road-access using route-finding within a harvest-scheduling optimization. I apply this model to two different representations of the road network: the Traditional Spatial Representation (TSR) where roads are modeled as arcs connecting nodes, and the Line Graph Representation where roads are modeled as nodes, and arcs represent shared intersections. This transformation retains the same information as the original network, but can alter the number of nodes and arcs in the system. I illustrate the mechanics of the model in a case study in the Pacific Northwest and show that the LGR was able to outperform the TSR in many of the tested scenarios.