Forest Planning Models Research Articles

The inclusion of improved forest management in strategic forest planning and its impact on timber harvests, carbon and biodiversity conservation

In forestry, although the so-called nature-based climate solutions have usually been focused on the calculation of carbon captured in new afforestation projects, it should be noted that the increase in carbon associated with improvements in their management (Improved Forest Management) can also be computed. This type of carbon is not usually integrated into strategic forest planning models, nor has its possible degree of conflict with other regulation ecosystemic services, like biodiversity conservation, been verified. In this research, those two issues have been approached by calculating a baseline in an emblematic forest with an extensive forestry history. For this purpose, we have designed two scenarios, i.e., one linked to its current management (Business As Usual, BAU) and another justified by the inclusion of Improved Forest Management (IFM). The results reveal a notable conflict between the carbon captured and the values of the indicators used to measure biodiversity. In order to reach a compromise between both scenarios, a multi-criteria model has been proposed that could be more attractive than the above ones. In addition, the carbon profit credits in the first ten years have been computed under the IFM scenario; the latter could be, a priori, an object of transaction in a voluntary carbon market. In conclusion, our model generates feasible solutions that allow the integration of IFM into strategic planning. Besides, those solutions show interesting tradeoffs between carbon and biodiversity. This discord must be distinguished by the current state of the forest and its expected growth, as well as their influence on the values associated with provision ecosystem services, such as the present net value associated with timber harvests.

A New Tree-Level Multi-Objective Forest Harvest Model (MO-PSO): Integrating Neighborhood Indices and PSO Algorithm to Improve the Optimization Effect of Spatial Structure

Accurate, efficient, impersonal harvesting models play a very important role in optimizing stand spatial structural and guiding forest harvest practices. However, existing studies mainly focus on the single-objective optimization and evaluation of forest at the stand- or landscape-level, lacking considerations of tree-level neighborhood interactions. Therefore, the study explored the combination of the PSO algorithm and neighborhood indices to construct a tree-level multi-objective forest harvest model (MO-PSO) covering multi-dimensional spatial characteristics of stands. Taking five natural secondary forest plots and thirty simulated plots as the study area, the MO-PSO was used to simulate and evaluate the process of thinning operations. The results showed that the MO-PSO model was superior to the basic PSO model (PSO) and random thinning model Monte Carlo-based (RD-TH), DBH dominance (DOMI), uniform angle (ANGL), and species mingling (MING) were better than those before thinning. The multi-dimensional stand spatial structure index (L-index) increased by 1.0%~11.3%, indicating that the forest planning model (MO-PSO) could significantly improve the spatial distribution pattern, increase the tree species mixing, and reduce the degree of stand competition. In addition, under the four thinning intensities of 0% (T1), 15% (T2), 30% (T3), and 45% (T4), L-index increased and T2 was the optimal thinning intensity from the perspective of stand spatial structure overall optimization. The study explored the effect of thinning on forest spatial structure by constructing a multi-objective harvesting model, which can help to make reasonable and scientific forest management decisions under the concept of multi-objective forest management.

Research on the optimal forest management strategy aiming at maximum carbon sequestration

In this paper, we use the 3-PG model to establish the relationship between time and carbon sequestration function, further analyze the relationship between forest age and carbon sequestration based on the 3-PG model, and obtain the optimal forest management strategy aiming at the maximum carbon sequestration. In addition, a fuzzy comprehensive evaluation (FCE) model is established to deduce the transition points between optimal forest planning models from the mean values under different conditions. Finally, we use the 3-PG model to estimate the carbon sink values after 100 years. We refer to the 3-PG model and FCE to illustrate the necessity of moderate deforestation, which is beneficial to forest development and carbon sequestration.

Integrating Habitat Quality of the Great Spotted Woodpecker (Dendrocopos major) in Forest Spatial Harvest Scheduling Problems

Biodiversity conservation has been broadly recognized in multi-objective forest management over the past decade. Nevertheless, habitat serves as one of the key influencing factors of biodiversity; while timber production and habitat quality are integrated into forest management operations, our knowledge about the trade-offs between the two is still limited. Thus, we formulated a habitat suitability index model for the great spotted woodpecker (Dendrocopos major) and developed a forest planning model that integrated timber revenue and habitat quality for a forest landscape in northeast China. We created three alternative management strategies, which spanned from timber benefit maximization to various management strategies restricted to differing amounts of suitable habitat. The results show that when the amount of suitable habitat comprised 39% to 65% of the landscape, this generated a 40.7% to 74.4% reduction in the total net present value, in comparison with the timber benefit maximization base scenario. The restriction of suitable habitat amount demands significantly decreased the total timber benefit in spatial planning problems. Our planning model provides an efficient approach to learning more about the trade-offs between timber production and wildlife habitat. Furthermore, the consideration of optimal habitat protection rather than increased habitat amount could be helpful for balancing targeting strategies among ecological and economic factors.

Simultaneous optimization of even flow and land and timber value in forest planning: a continuous approach

BackgroundForest management planning involves deciding which silvicultural treatment should be applied to each stand and at what time to best meet the objectives established for the forest. For this, many mathematical formulations have been proposed, both within the linear and non-linear programming frameworks, in the latter case generally considering integer variables in a combinatorial manner. We present a novel approach for planning the management of forests comprising single-species, even-aged stands, using a continuous, multi-objective formulation (considering economic and even flow) which can be solved with gradient-type methods.ResultsThe continuous formulation has proved robust in forest with different structures and different number of stands. The results obtained show a clear advantage of the gradient-type methods over heuristics to solve the problems, both in terms of computational time (efficiency) and in the solution obtained (effectiveness). Their improvement increases drastically with the dimension of the problem (number of stands).ConclusionsIt is advisable to rigorously analyze the mathematical properties of the objective functions involved in forest management planning models. The continuous bi-objective model proposed in this paper works with smooth enough functions and can be efficiently solved by using gradient-type techniques. The advantages of the new methodology are summarized as: it does not require to set management prescriptions in advance, it avoids the division of the planning horizon into periods, and it provides better solutions than the traditional combinatorial formulations. Additionally, the graphical display of trade-off information allows an a posteriori articulation of preferences in an intuitive way, therefore being a very interesting tool for the decision-making process in forest planning.

A learning heuristic for integrating spatial and temporal detail in forest planning

AbstractWe present a learning heuristic using dynamic programming (DP) formulations to address both spatial and temporal detail in multiobjective forest management planning. The problem is decomposed into smaller problems to avoid the curse of dimensionality associated with DP. The heuristic learns from multiple decomposed problem formulations to identify stands assigned the same management option regardless of formulation. Consistently managed stands are recognized, and the problem is eventually distilled to the most difficult to solve portions of the forest. The heuristic is demonstrated on a forest management problem with short‐lived core area wildlife habitat, where temporal detail is important. The problem is large due to the number of stand‐level management timing options and associated interactions with the management timings of nearby stands. Results show solution improvement along with substantial time savings over previously used heuristics. The learning heuristic enables analysis of large problems that emerge with high levels of spatial and temporal detail.Recommendations for Resource Managers: Adding spatial and temporal detail to forest planning models can improve the utility of the solution for some applications such as wildlife habitat management. Decomposing a large optimization problem into linked, smaller subproblems can speed the solution search time. Learning from problem decomposition solutions to formulate subsequent search attempts can improve the quality of a solution.

Habitat amount and connectivity in forest planning models: Consequences for profitability and compensation schemes

Adjacency relationships are pervasive in forest planning problems, especially the ones related to the selection of habitat networks for biodiversity conservation. Two main approaches are applied in the planning of these conservation actions: i) selection grounded on the island biogeography theory, where connected habitats are preferred and ii) selection grounded in the habitat amount hypothesis, where the amount of habitat is enforced in local landscapes, regardless of their spatial distribution. Because the presence of connectivity requirements in the creation of habitat networks impose more stringent limitations on the search for optimal solutions, they are expected to cascade to the total benefit from harvesting revenues and, consequently, to the costs of the habitat networks. The ecological implications of these approaches have been investigated, whereas the economic consequences of imposing connectivity remain unclear. Here, I address this issue and investigate the costs of selecting habitat networks in multiple forest landscapes in central Europe, applying these two approaches. To this end, a conic optimization model is proposed, to find minimum cost allocations of forest reserves. Furthermore, a sensitivity analysis on the optimal allocation is conducted, regarding the size of the habitat network required and the level of heterogeneity in forest profitability within the landscapes. The results show that habitat networks amounting to 10% of the forest area may be created with up to 5.5% reduction in the total Net Present Value (NPV), with a higher cost when connectivity is imposed (6.5%). The cost of connectivity, however, may increase in landscapes with high heterogeneity in forest profitability and with the minimum amount of habitat required. In conclusion, habitat selection must be tailored to local conditions and weight the additional costs of imposing connectivity against the requirements of the target species and the expected ecological benefits.

Uma perspectiva histórica do desenvolvimento de modelos de planejamento florestal com ênfase no nível operacional

The application of operations research techniques has led to a substantial improvement in the economic and ecologic efficiency of forest management, both for planted and natural forests. Forest planning addresses problems in different hierarchical levels that involve specific planning horizons and formulation complexity. This study proposes an historical perspective on the development of forest planning models in the last five decades, with a focus on the operational level. The emergence of operations research applied to forest planning problems can be dated back to the 60’s, with an intensification of this line of research on the 80’s and 90’s, accompanying the fast development on the available computing power. In the 90’s, forest planning problems started to be classified according to hierarchical levels in strategic, tactical and operational. While the strategic and tactical levels address decisions on the long- and medium-term, the operational level deals with short-term decisions, typically involving harvesting machinery allocation and transportation of forest products. In this sense, the operational planning is characterized by a high level of complexity of the planning models and economic importance to forest management. We conclude that despite the increasing number of publications related to forest planning, the operational level remains underrepresented and efforts to integrate decisions across the different hierarchical levels of forest planning are required.

Combining biophysical and socioeconomic suitability models for urban forest planning

Urban forests are landscape mechanisms that provide ecosystem services and positive health benefits. However, many urban areas lack canopy coverage and continue to lose coverage through land cover change and tree mortality. In the United States, neighborhoods dominated by lower socioeconomic incomes (<US$24,000 median household income) are largely devoid of mature tree canopy cover, which compounds existing socioeconomic issues such as preventable adverse health conditions. This project demonstrates how geospatially combining biophysical attributes with socioeconomic conditions can be used to preliminarily identify opportunities for tree canopy enhancement and establishment, specifically in Lexington, Kentucky (USA). Using ESRI’s ArcGIS and publicly available data, a raster weighted overlay suitability modeling approach was used to combine ten biophysical and socioeconomic factors to identify first-pass planting site opportunities. A visual accuracy assessment using aerial imagery and field inspection of model results indicated that the approach was identifying sites conducive to planting trees. In general, the suitability approach often identified relatively small areas for planting opportunities. This approach provides a starting point for community involvement regarding municipality specific model development and implementation. With this flexible suitability modeling approach, we demonstrate how a community can combine biophysical and socioeconomic data in a planting site selection approach to meet local conditions and desires for tree planting strategies.

Balancing forest profitability and deadwood maintenance in European commercial forests: a robust optimization approach

This study seeks to include two central aspects of forest management into an optimized forest planning model for commercial European forests: (i) the uncertainty related to climate change and forest responses to new environmental conditions and (ii) the maintenance of deadwood on forest stands, essential for sustaining biodiversity and promoting forest resilience. We analyzed forest outcomes of alternative management regimes generated by the process-based model 4C, considering four climate change scenarios. We evaluated the impacts on forest economy caused by an increasing amount of deadwood biomass left on forest stands, applying a deterministic and a robust forest planning model. Our results show that areas with high growth rates and low wood prices display the lowest trade-off between profitability and deadwood maintenance, whereas regions with high wood prices display high opportunity costs for maintaining large amounts of deadwood. Moreover, selecting robust management regimes caused minor impacts on the NPV, with an average reduction of 7% compared to the deterministic optimal solutions, appearing as a suitable alternative for integrating climate uncertainty into forest management planning.

A value-added forest management policy reduces the impact of fire on timber production in Canadian boreal forests

When fire rates are sufficiently high, fire disturbances can have negative impacts on industrial timber supplies. One can mitigate such problems at the strategic level by accounting for potential fire losses in the timber supply planning process by reducing harvest levels to maintain a buffer stock of timber. With a forest planning model based on a timber volume maximizing policy, reducing the harvest level will lead to a reduction in the harvested timber volume and likely, of revenues. One possible solution is to change the policy to increase the value of the wood that is harvested so as to minimize such reductions with less risk. We have evaluated alternative policies for three commercially-managed forests that have different burn rates in northeastern Canada. When compared with a volume-maximization policy, a revenue-maximization policy that considers sustained production and the sale of sawmilling wood products (lumber, chips and sawdust) increased mean revenues by 130% (36–770%) with >0.90 probability and substantially decreased the area and volume harvested by 27% (11–38%) and 28% (14–36%), respectively. By reducing the harvest volume, the total number of jobs associated with forest operations decreased by 20% (10–27%) but the number of jobs per unit area harvested and volume increased. The policy also increased the harvest age and thereby enhanced the retention of a greater proportion of old-growth stands. Our study indicated that a tighter link between strategic planning and wood product processing helped identify better compromises between harvesting activities and revenues, despite the occurrence of natural disturbances.

Developing alternative forest spatial management plans when carbon and timber values are considered: A real case from northeastern China

Forest ecosystems play an important role in mitigating global climate change, and this role has recently been further reinforced by the Paris Agreement. However, our knowledge with respect to the trade-offs between timber production and carbon sequestration in forest ecosystems is still seriously deficient. Therefore, the overall goal of this study is to quantitatively analyze the effects of a set of economic and ecological constraints on the joint production capacity for forest timber and carbon by alternative forest management strategies for a large forest in northeastern China. The proposed forest planning models integrate four alternative forest management strategies, namely, the timber-oriented management strategy (TMS), the carbon-oriented management strategy (CMS), the multiobjective management strategy (MMS), and the resource-restricted management strategy (RMS). Four different planning scenarios for each strategy were further generated by successively adding one additional constraint, which mainly included the even-flow of timber production, the adjacent constraints of harvest activities, and the minimum targets of carbon sequestration, over a 50-year planning horizon. The results showed that increasing the prices of carbon resulted in positive quadratic polynomial total and carbon net present values (NPVs), positive logistic carbon sequestration and stocks, and negative logistic harvest of timber and its NPV for optimal forest management plans, in which the carbon price of $100 per ton was a significant threshold for balancing the harvest of timber and carbon sequestration. In addition to the CMS, our tested spatial and nonspatial constraints all showed significant effects on optimal forest management plans when a realistic carbon price (i.e., $20 ton−1) from the carbon trading market in China during 2014–2017 was employed, in which decreases of approximately 29.34% and 25.08% were observed for total NPV when twenty-percent deviations in harvest volume between any two consecutive periods were employed. Additionally, two periods of green-up constraints could further reduce the total NPV by approximately 17.87% and 15.73% for TMS and MMS, respectively, when compared with their base scenarios. However, increasing the minimum carbon target by one percent reduced the total NPV by approximately $29.44 per hectare per year when evaluated for RMS. Our optimization framework not only can be replicated in other regions with similar characteristics but also contributes to the ongoing debate about the trade-offs between carbon sequestration and wood production benefits.

SPATIAL MODELING OF TRANSPORT DEVELOPMENT OF FOREST AREA AND THEIR POTENTIAL ENVIRONMENTAL RISKS

Permanentattributesoftimberharvestingareanumberofpotentialenvironmentalrisks, eachofwhichcancausesignificantdamagetotheenvironment. The intensive development of technology and the improvement of industrial production processes have led to a significant increase in technogenic impact both on increasing catastrophic natural disasters and on the global climate change formation. The adoption of the World Environmental Constitution by all the states would be an effective means of regulating and minimizing these negative processes. Timber harvesting is one of the most dangerous types of technogenic impact on the forest environment, as the forest stand, young growth, natural watercourses and soil are damaged during logging and transportation. However, the degree of the negative impact of timber harvesting can be reduced to an ecologically acceptable level, and technical indicators of the use of timber-hauling machinery can be brought to economically feasible values by properly assessing the intensity of the environmental risk of taking a decision on certain technical and technological issues and the implementation of environmental management of this process. The article presents some approaches to the creation of GIS spatial planning model of transport development of forest-exploitation area based on the cost estimation of timber skidding considering technogenic impact of forest machines. The development of the model of forest transportation planning is a complex task. In order to solve this task, the system under investigation should be divided into separate interconnected modules, each acting as its own model: the models for forest transportation planning, the database, formulation of the task, the results of modeling, an analysis of transport movement possibilities, an analysis of environmental damage, the assessment and improvement of the existing forest road network. Concerning the proposed model and methodology that is based on the analysis of potential environmental risks associated with the rutting and cost-assessment of timber skidding, we have obtained the model map of environmentally-acceptable types of timber-hauling machines for a real forest exploitation area, the Rozhanka forest district, the Slavsk State Forestry Enterprise in particular. The proposed model makes it possible to substantiate environmentally safe and economically feasible ways of skidding, estimate the ratio of transport development of a forest area using various terrestrial technical means (wheeled and crawler tractors or cable systems), as well as to outline the possible occurrence, intensity and spread of environmental hazards associated with timber harvesting.

Incorporating uncertainty into forest management planning: Timber harvest, wildfire and climate change in the boreal forest

In an effort to ensure the sustainability of their forests, boreal forest managers often use forest planning models to make future projections of timber supply and other key services, such as habitat for wildlife. Projecting the fate of these services has proven to be challenging, however, as major uncertainties exist regarding the principal drivers of boreal ecosystem dynamics, including the future spatial and temporal distribution of wildfire and timber harvesting. Existing forest planning models are not well suited to dealing with this uncertainty because they produce deterministic projections based on central tendencies of these drivers.Here we present a new approach for incorporating uncertainty into forest management planning, which we demonstrate using two landscapes in the Canadian boreal forest. Our approach takes the assumptions contained within the latest forest management plans for each of these landscapes, including parameterizations of their deterministic forest planning models, and converts these assumptions into equivalent parameterizations of a stochastic, spatially-explicit state-and-transition simulation model (STSM). We then use Monte Carlo simulations with the STSM to “stress-test” the forest management plan with respect to a range of possible future uncertainties, including uncertainties in future levels and patterns of wildfire and timber harvest, along with the possible changes in wildfire that might result from future climate change.Our analysis demonstrates the importance of incorporating stochastic variability into projections of future ecosystem condition. The STSM projections that acknowledged variability in wildfire and timber harvest differed from the deterministic forest planning model projections that were based solely on mean values. Our analysis also suggests that there is an increased risk of shortfalls in timber harvest, for both boreal landscapes, associated with future projections for changes in wildfire due to climate change, and that management strategies aimed at reducing the future level of timber harvest offer an opportunity to mitigate these risks. We believe our approach provides a new risk-based framework for incorporating uncertainty into forest management, including the effects of climate change.

Heuristic forest planning model for optimizing timber production and carbon sequestration in teak plantations

We developed a forest planning model integrating two operational scales (single-stand and forest levels) for the optimization of timber production and carbon sequestration in forest teak (Tectona grandis L. f.) plantations. At the stand level, growth and yield simulations using a heuristic thinning optimizer provided a set of near-optimal thinning regimes for individual stands differing on initial spacing and site quality, given biological, silvicultural, and financial constraints. The set of near-optimal thinning regimes obtained were then used as input of the forest-level model, which generated optimal harvest plans for the whole plantation by simultaneously maximizing the net present value of merchantable wood and carbon sequestration. The net amount of carbon captured by the biomass and the emissions produced by decomposition of woody debris and timber products after harvest were estimated. The growth and yield model was based on a system of differential equations incorporating heuristics (genetic algorithms) to optimize age and intensity of thinnings. The full model can handle the optimization of harvest schedules for projects up to 10.000 ha and 200 stands and was tested on a validation dataset including teak plantations from Venezuela and other Latin American countries. Results indicated that regimes favoring carbon sequestration reduce the benefits of timber production, and equal profitability of carbon sequestration and timber production was obtained for carbon prices over 40 $US Gg-1. Sensitivity analysis showed that the proposed model is sensible to variation in growth rates, carbon and timber prices, and production quotas, and barely sensible to harvest and transport costs. The developed model has a modular structure that allows its calibration to incorporate data from a wide range of management regimes for teak and other forest species.

Comparing the efficacy of linear programming models I and II for spatial strategic forest management

Contemporary strategic forest management goals have become increasingly complex in spatial definition and scale. For example, the Canadian Council of Forest Ministers Criteria and Indicators (CCFM C&amp;I) includes metrics that are expressed at multiple levels of spatial resolution such as ecodistricts, watersheds, and vegetative communities. Supporting these criteria with aspatial models is sometimes difficult, and results are often not transferable to the actual forest. We describe a spatial Model I stand and prescription-based strategic forest planning model that includes spatial metrics in a realistic sized problem. We compare its formulation, capabilities, and computational efficiency with a Model II formulation using a case study on Nova Scotia’s Crown Central Forest. We demonstrate that the spatial Model I is better suited to support strategic forest management when spatial criteria are included.

Promoting harvesting stands connectivity and its economic implications in Brazilian forest plantations applying integer linear programming and simulated annealing

The spatial allocation of harvesting activities is a challenging task for forest managers, given the complexity of coordinating operations and the great contribution of harvesting to the total cost of wood production. Traditionally, forest harvesting policies have intended to limit maximum clear-cut areas, leading to harvesting fragmentation, and have thus reduced interior forest habitat and negatively affected operational efficiency. Aiming to address this issue, the main goals of this study were i) to propose approaches to include harvesting connectivity into a forest planning model, and ii) to evaluate the impacts of enforcing connectivity on the economic outcomes of the forest. We applied two approaches for clustering forest harvesting: (i) a model based on the Minimum Spanning Tree problem for enforcing harvesting connectivity and (ii) a Simulated Annealing approach for simultaneous consideration of harvesting stands connectivity and wood flow. The optimization process could reduce the average harvesting radius from 4575.8 up to 2300.5m and increase the average area of harvesting blocks from 22.4 up to 157.4ha. However, this solution would marginally reduce the net present values (from 3.9% to 15.4%) compared to the base scenario, without the inclusion of connectivity requirements and depending on the level of enforced connectivity.

Assessing biodiversity and conservation status of the Natura 2000 forest habitat types: Tools for designated forestlands stewardship

The maintenance of biodiversity in forestlands has become one of the major concerns of forestry in the European Union (EU) as well as globally. The EU and its member states implement it through the Forest Europe process, which promotes sustainable forest management, and the EU Council Habitats Directive (HDirective). Within the Forest Europe process, indicators and management concepts are developed for forests in general, whereas the HDirective is concerned with the forest habitats and forest habitat types of the Natura 2000 network. Although the HDirective helps to tackle a broad range of biodiversity problems, there remain some open issues, including the vaguely defined concept of a forest habitat type, conservation status of a forest habitat type, lack of defined indicators of conservation status and undeveloped concepts for the stewardship of forest habitat types. This study addressed most of these open problems. The methods were tested in three habitat types in Slovenia: 9110 – Luzulo-Fagetum beech forests, 91K0 – Illyrian Fagus sylvatica forests (Aremonio-Fagion) and 91L0 – Illyrian oak–hornbeam forests (Erythronio-Carpinion). To make the definition of a forest habitat type more concrete, a hierarchical order was introduced into the current concept of forest habitat types. A hierarchal relation between forest habitat types and their subtypes was established by employing a bottom-up strategy and classification key. This key was developed through exploring the vegetation and eco-geographical characteristics of the forest habitat subtypes. An assessment of the conservation status of forest habitat types was performed using 18 indicators. Only the indicators supporting the favorable conservation status definition outlined in the HDirective were selected. The stewardship of forest habitat types was demonstrated through assessment points depicting the present, ideal and desired states of the indicators. The points were constructed through a basic statistical analysis, vegetation and forest planning models and literature review. The results showed that dividing the three forest habitat types produced less heterogeneous forest habitat subtypes. The indicators and the assessment points performed well as they suggested the preferred course of development of the three forest habitat types. Because of their applicability in different environments, the methods can be used in other European countries and regions and beyond.

Spatially constrained harvest scheduling for multiple harvests by exact formulation with common matrix algebra

Exact formulations currently developed for spatially constrained harvest scheduling problems mostly consider only a single harvest over time for individual forest units. We propose a new method for formulating the scheduling problem of allowing multiple harvests over time by using common matrix algebra. We combine the concept of Model I formulation, which defines treatments to overcome issues of multiple harvests, with that of adjacency constraints for treatments. Conflicting harvests over space and time are resolved by introducing two kinds of adjacency matrices. One is an ordinary spatial adjacency matrix for the forest unit location, and the other is a newly introduced activity adjacency matrix to identify concurrent harvesting activities in a set of possible treatments for one forest unit. The Kronecker product of these two adjacency matrices is used to generate the entire adjacency constraint for treatments among all forest units to avoid adjacent harvests. The advantage of our approach is that it relies on the concept of the Model I formulation to satisfy spatial restrictions and identify decision variables for treatments of all forest units systematically using common matrix algebra, so that conversion and extension of existing non-spatial forest planning models (e.g., FORPLAN) to consider multiple harvests and green-up constraints can easily be achieved in a spatially explicit manner.

Temporal Connectivity of Mature Patches in Forest Planning Models

Temporal Connectivity of Mature Patches in Forest Planning Models