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

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.

Use of Optimization Modeling to Assess the Effect of Timber and Carbon Pricing on Harvest Scheduling, Carbon Sequestration, and Net Present Value of Eucalyptus Plantations

Quantifying the impact of carbon (C) and timber prices on harvest scheduling and economic returns is essential to define strategies for the sustainable management of short-rotation plantations so that they can provide timber products and contribute to C sequestration. In this paper, we present a mixed-integer linear programming model that optimizes harvest scheduling at the forest level, C sequestration, and Net Present Value (NPV) over a planning period of up to 15 years. The model included revenue from the sale of timber (pulplogs) and credits from the net C sequestered during the life of the stands. In addition, plantation establishment, management, harvesting, and transportation costs were included in the analysis. The study area comprised 88 Eucalyptus grandis W. Hill and Eucalyptus dunnii Maiden stands located in Uruguay, totaling a forest area of nearly 1,882 ha. The study investigated the impact of C and timber prices on NPV, harvest schedules, stands’ harvest age, timber flows to customers, and C sequestered per period. The maximum NPV among all the scenarios evaluated (USD 7.53 M) was calculated for a C price of 30 USD t−1, an interest rate of 6%, and a timber price of 75 USD m−3. This was USD 2.14 M higher than the scenario with the same parameters but that included only revenue from timber. C prices also impacted stands’ harvest age, C sequestration, and timber flows delivered to end customers. On average, in scenarios that included C prices, timber flows and C sequestration increased by 15.4 and 12.1%, respectively, when C price increased from 5 to 30 USD t−1. These results demonstrate that harvest scheduling, harvest age, and NPV are very sensitive to C and timber, and that the best economic returns are obtained when the stands are managed to maximize timber production and C sequestration.

Evaluating Long-Term Seedling Growth across Densities Using Nelder Plots and the Forest Vegetation Simulator (FVS) in the Black Hills, South Dakota, USA

Small-tree development affects future stand dynamics and dictates many ecological processes within a site. Accurately representing this critical component of stand development is important for evaluating treatment alternatives from fuel hazard reduction to harvest scheduling. As with all forest growth, competition with other vegetation is known to regulate small-tree growth dynamics. This study uses three Nelder plots with 45 years of ponderosa pine growth to understand competition effects on seedling growth and evaluate the Forest Vegetation Simulator (FVS) Central Rockies (CR) variant’s ability to represent these dynamics. Removal of herbaceous competition before planting increased tree diameters by 50–135% and height by 35–75% across a planting density gradient at age 12. However, by age 45, the effect of herbaceous competition on tree size was no longer evident. Instead, trees at the lowest planting density had diameters 2.5–3 times larger than the most densely grown trees. Forest Vegetation Simulator (FVS) simulations underpredicted diameter at breast height (dbh) by 35–50% and 0–35% for 12 and 45-year-old trees, respectively. There was an underprediction bias of 15–20% for heights at age 12 and overpredictions of 5–10% at age 45. Continuous underprediction of dbh will affect the reliability of modeled fuel treatment longevity and sustainable harvest scheduling. Study Implications: Management and modeling of small-tree growth can affect decision-making for a range of activities, from assessing fuel treatment effectiveness to sustainable harvest scheduling. Effective small-tree density management can increase tree diameters at age 45 by 2.5–3 times the diameter of unthinned sites. FVS-CR underpredicted age 12 heights by 0–45% and age 45 diameters by 0–35% as a function of planting density, suggesting that the model fails to capture the intensity or timing of density-induced competition. These underpredictions will inflate the length of time fuel treatments remain effective and decrease projected sustainable harvest levels supported by responsible management.

An MILP Model for Corn Planting and Harvest Scheduling Considering Storage Capacity and Growing Degree Units

Corn planting and harvest scheduling is an important problem due to having a significant impact on corn yield, balancing the capacities for harvest, transport, and storage operations. Different corn hybrids also have different planting window and poor planting and harvest schedules may cause erratic weekly harvest quantities and logistical and productivity issues. In the 2021 Syngenta Crop Challenge, Syngenta released several large datasets that recorded the historical daily growing degree units (GDU) of two sites and provided planting window, required GDUs, and harvest quantity of corn hybrids planted in these two sites. Then, participants of this challenge were asked to schedule planting and harvesting dates of corn hybrids under two storage capacity scenarios so that facilities are not over capacity in harvesting weeks and have consistent weekly harvest quantities. The two storage capacity scenarios include: (1) planting and harvest scheduling given the maximum storage capacity, and (2) planting and harvest scheduling without maximum storage capacity to determine the lowest possible capacity for each site. In this paper, we propose two mixed integer linear programming (MILP) models for solving this problem considering both the storage capacity and the uncertainty in GDUs. Our results indicate that our proposed models can provide optimal planting and harvest scheduling under different GDU possibilities which ensures consistent weekly harvest quantities that are below the maximum capacity.

Assessing the Impact of 41 Years of Forest Management on Native Wildlife Habitat in Minnesota, USA

Over the last four decades, forest management goals have transitioned to multiuse objectives, begging the question of their impact on wildlife habitat. Using USDA Forest Service Forest Inventory and Analysis data and the WHINGS (Wildlife Habitat Indicator for Native Genera and Species) model, the trends in wildlife habitat were quantified from 1977 to 2018 across Minnesota. Statewide, 35.5% of species experienced significant improvement in habitat, 29% significant reductions, and 35.5% nonsignificant change. The extent of habitat (acreage) increased for 100% of species, but the quality declined for 63% of species. Results were explained by the reduction in acreage of larger size classes of the aspen, balsam, and birch forest type and increases in smaller, younger forest area. Specifically, forest management that converted aspen stands to other forest types benefited certain wildlife species over others. Future forest management should consider the balance between the habitat requirements of the diverse native species in Minnesota. Study Implications Trends in forest wildlife habitat over the last four decades across Minnesota highlight that forest management often favors one species at the expense of another. Statewide, wildlife species with preferences for larger, older aspen experienced diminished habitat, whereas habitat for species preferring younger forest types or older nonaspen types increased. Regionally, the forested ecoregions in Minnesota (northeast) generally saw reduced habitat, whereas the prairie/agricultural regions (south and northwest) saw the largest increases. Through this and further applications, forest and wildlife managers can rapidly assess the habitat implications of proposed management, whether for environmental review, forest planning, or harvest scheduling.

A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

Comparison of Spectral Reflectance-Based Smart Farming Tools and a Conventional Approach to Determine Herbage Mass and Grass Quality on Farm

The analysis of multispectral imagery (MSI) acquired by unmanned aerial vehicles (UAVs) and mobile near-infrared reflectance spectroscopy (NIRS) used on-site has become increasingly promising for timely assessments of grassland to support farm management. However, a major challenge of these methods is their calibration, given the large spatiotemporal variability of grassland. This study evaluated the performance of two smart farming tools in determining fresh herbage mass and grass quality (dry matter, crude protein, and structural carbohydrates): an analysis model for MSI (GrassQ) and a portable on-site NIRS (HarvestLabTM 3000). We compared them to conventional look-up tables used by farmers. Surveys were undertaken on 18 multi-species grasslands located on six farms in Switzerland throughout the vegetation period in 2018. The sampled plots represented two phenological growth stages, corresponding to an age of two weeks and four to six weeks, respectively. We found that neither the performance of the smart farming tools nor the performance of the conventional approach were satisfactory for use on multi-species grasslands. The MSI-model performed poorly, with relative errors of 99.7% and 33.2% of the laboratory analyses for herbage mass and crude protein, respectively. The errors of the MSI-model were indicated to be mainly caused by grassland and environmental characteristics that differ from the relatively narrow Irish calibration dataset. The On-site NIRS showed comparable performance to the conventional Look-up Tables in determining crude protein and structural carbohydrates (error ≤ 22.2%). However, we identified that the On-site NIRS determined undried herbage quality with a systematic and correctable error. After corrections, its performance was better than the conventional approach, indicating a great potential of the On-site NIRS for decision support on grazing and harvest scheduling.