The application of optimization methods to forest management has given rise to a successful line of investigation in recent decades. However, there have been few publications associated with the ...application of these techniques to the management of industrial forest plantations (those with short or medium rotations, always less than 50 years), which consider the important role played by these forest systems in the supply of diverse goods and services. This study presents an overview of this literature which, by analyzing 67 articles published in journals contained in the ISI Web of Science, highlight, among other aspects, the techniques employed, their evolution, their planning type (strategic, tactical or operational), the functional objectives and constraints considered, or the type of software deployed in these studies. The results show how Model I has been the one most frequently used in these studies, and how the spatial component is increasing in importance. However, classic optimization methods, such as mixed integer programming, have been those most commonly resorted to, although the employment of multi-criteria techniques such as goal programming and analytic hierarchical process have strongly emerged in recent years.
We developed and applied a spatial optimization algorithm to prioritize forest and fuel management treatments within a proposed linear fuel break network on a 0.5 million ha Western US national ...forest. The large fuel break network, combined with the logistics of conducting forest and fuel management, requires that treatments be partitioned into a sequence of discrete projects, individually implemented over the next 10–20 years. The original plan for the network did not consider how linear segments would be packaged into projects and how projects would be prioritized for treatments over time, as the network is constructed. Using our optimization algorithm, we analyzed 13 implementation scenarios where size-constrained projects were prioritized based on predicted wildfire hazard, treatment costs, and harvest revenues. We found that among the scenarios, the predicted net revenue ranged from USD 3495 to USD 6642 ha−1, and that prioritizing the wildfire encounter rate reduced the net revenue and harvested timber. We demonstrate how the tradeoffs could be minimized using a multi-objective optimization approach. We found that the most efficient implementation scale was a sequence of relatively small projects that treated 300 ha ± 10% versus larger projects with a larger treated area. Our study demonstrates a decision support model for multi-objective optimization to implement large fuel break networks such as those being proposed or implemented in many fire-prone regions around the globe.
ABSTRACT The aim of this study was to develop a mathematical model for the spatial forest planning of harvest activity scheduling. Thirty-eight (38) blocks were formed from stands aged 13 to 17 years ...considering a total area limit set to 350 hectares. The model was built in Excel ® spreadsheet and solved by CPLEX® optimization software using the Branch and bound method for the linear programming of problems with integer variables. The results of optimization are presented in the form of a map of spatial distribution of the selected blocks. The total harvested area was 5,989 hectares and the volume generated was 2,956,913 m3 in a planning horizon of five years. Higher results compared with those of traditional planning and efficiency to optimize forest harvesting proved to be a viable alternative to the inclusion of space and operational issues associated with forest harvesting.
ABSTRACT In industrial forest plantations, the spatial distribution of management units for harvest scheduling influences the timber production cost and the non-renewable resources consumption, due ...to issues related to transport logistic. In this context, this research aimed to formulate Integer Linear Programming (ILP) by means of the application of Floyd-Warshall network optimization algorithm to generate timber production routes, minimizing the production costs resulting from harvest activities and forest road maintenance. Then, scenarios were simulated considering different minimal harvest ages for Pinus spp. and Eucalyptus spp. stands. The planning horizon was five years with annual periodicity. The study area was 23,330 hectares of forests, located in Paraná state (southern Brazil). We compared the simulated scenarios according to the following parameter indicators: harvest income, building road network and the production unit cost. The decreasing of the minimal harvest age reduces the mean production of management units scheduled to be harvested, in other hand, it requires fewer roads to be built, and consequently increases the production unit cost. The solutions obtained by using ILP models presented an optimality gap lower than 0.1%.
RESUMO Nas plantações florestais industriais, a distribuição espacial das unidades de manejo agendadas para colheita influencia o custo de produção madeireira e o consumo de recursos não renováveis, devido às questões relacionadas com a logística de transporte. Neste contexto, o objetivo do estudo foi formular modelos de Programação Linear Inteira (PLI) por meio da aplicação do algoritmo de otimização em redes Floyd-Warshall na geração de rotas de produção madeireira, minimizando o custo de produção resultante das atividades de colheita e manutenção de estradas. Em seguida, foram simulados cenários considerando distintas idades mínimas de corte de talhões de Pinus spp. e Eucalyptus spp. O horizonte de tempo foi de 5 anos com periodicidade anual. A área de estudo foi 23.330 hectares de florestas, localizados no estado do Paraná (sul do Brasil). Nos comparamos os cenários simulados de acordo com os seguintes parâmetros indicadores: rendimento da colheita, rede de estradas utilizada e custo unitário de produção. A diminuição da idade mínima de corte reduz a produtividade média das unidades de manejo agendadas para colheita e, por outro lado, requer menos estradas edificadas, o que consequentemente diminui o custo unitário de produção. As soluções obtidas pelo uso dos modelos PLI estiveram menos de 0,1% distantes do ótimo global.
Recent extreme wildfire seasons in the United States (US) have rekindled policy debates about the underlying drivers and potential role forest management can play in reducing fuels and future ...wildfire. Most US western national forests face a substantial backlog of treatments and manifold management issues related to wildfire, forest health, and wildfire protection and constitute the major part of the wildfire problem. However, the precise schedule and detailed assessments that map the type and amount of treatments needed, as well as the associated cost are rarely assessed. We simulated restoration trajectories on the US fire prone Umatilla National Forest that faces complex management challenges related to wildfire and forest resiliency. The treatments were targeted to specific ecological conditions based on a decision tree developed in consultation with specialists. Planning areas were then prioritized based on fire protection of the wildland-urban interface (WUI), forest products, and stand resiliency. The results revealed a backlog of 211,893 ha, that when treated would generate $320 million in revenue from forest products, and cover 80% of the forest. The treatment area estimate was more than double prior estimates based on ecological departure from historic condition. Financial sensitivity analysis showed that high priority fuel treatments were revenue positive on 22% of the planning areas. The study established a restoration blueprint in terms of amount, location, and treatment type to support funding requests to the agency and schedule internal and external capacity to complete the work. The work also contributes to ongoing collaborative restoration planning to help stakeholders understand the opportunity cost of specific restoration objectives. The case study and framework can be widely extrapolated to the national forests in the western US to improve financial evaluation of forest and fuel management and estimate future management inputs. This work represents a rare instance of a bottom-up spatially explicit assessment of a restoration backlog, and prioritization of planning areas to reduce that backlog on a US national forest.
•Estimates of forest restoration needs are a key input into US federal forest policy.•Heretofore, restoration needs have been based on fire regime and ecological departure.•We used an alternative approach based on silvicultural treatment decision trees.•The approach doubled the estimated treatment needs compared to ecological assessment.•Revenue from harvesting was insufficient to pay for needed surface fuels treatment.
Active forest restoration programs on western US national forests face multiple challenges to meet their broad ecological goals while designing projects that generate sufficient revenue to build and ...maintain private forest management capacity needed to expand the scale and scope of treatments. We explored ways to design projects where admixing of treatments along gradients of dry and moist mixed conifer forest types could maximize financial viability while including substantial area where broadcast burning could be applied in conjunction with other treatments. In general, we found that restoration treatments in dry forests that included density reduction thinning and broadcast burning resulted in a net projected cost ranging from $110 to $8000 per ha. By contrast, density reduction thinning in moist mixed conifer forests on more productive microsites generated significant commercial timber volume and projected revenue that ranged from $4000 to $20,000 per ha. We used spatial optimization methods to identify potential project areas that maximized revenue while meeting constraints to treat a minimum proportion of each project with broadcast burning. Multiple project area sizes were also explored to understand the effect of restoration scale on financial outcomes. We found that optimal projects in terms of generating revenue to subsidize density reduction and broadcast burning were 810 ha and contained >50% dry forest area. Larger projects and those with a higher percentage of dry forest area resulted in lower revenue, eliminating revenue when projects reached 2700 ha. Forest restoration programs can use these methods to plan and design restoration projects that are financially viable while addressing the broadcast burn backlog in dry forests that require relatively expensive fuel reduction treatments prior to re-introducing fire.
Abstract
Forest-management planning could be addressed at various temporal scales, namely strategic and tactical scales. The former are associated with extended temporal horizons, whereas the latter ...focus on shorter periods of time and typically encompass further spatial requirements. On the other hand, in most forestry scenarios, the existence of multiple criteria of different nature is the rule rather than the exception. It seems sensible to think that forest-management models would significantly increase their practicality in many cases, if the strategic and tactic models were to be integrated within a multicriteria context. This paper presents an integrated framework for dealing with this type of situation. Thus, two approaches called “top down” and “integrated” have been formulated. To undertake this task, the well-known tool called extended goal programming has been resorted to. The functioning and the strengths of the integrated framework are illustrated with a case study corresponding to fast-growing plantations in Brazil. This framework includes the decisionmaker’s preferences in a more compact model that allows the inclusion of different spatial issues.
ABSTRACT The aim of this paper was to evaluate different criteria for stem measurement sampling and to identify the criterion with best performance for developing individual tree volume equations. ...Data were collected in eucalyptus stands 58 to 65 months old. Schumacher-Hall model was applied using five sampling criteria with nine variations (45 in total): 1) number of trees per diameter class, being (a) fixed number, (b) proportional to the diameter class of the sample, or (c) proportional to the standard deviation of the sample; and 2) the width of the diameter class, which ranged from 1.0 up to 5.0 cm. We used the equations generated from each of the five sampling criteria to estimate stem volume of trees reserved for validation. This allowed us to obtain standard errors of estimates from this data-set. In addition, residuals of volume estimates were examined by means of statistical tests of bias, autocorrelation and heteroscedasticity. Better performances of volume equations occurred when smaller diameter class widths were used, i.e., when the sample size increased. There was no clear trend in increasing/decreasing residual autocorrelation and/or heteroscedasticity. Both methods of sampling proportional to the frequency of diameter class had the best performances, inclusive using only 36 trees. The ones where choice of trees was proportional to the standard deviation had the worst. In conclusion, the selection proportional to the frequency of the diameter class, under the condition that at least two trees per class are sampled, provides models statistically better than all the other criteria.
RESUMO O objetivo deste trabalho foi avaliar diferentes critérios para amostragem de fustes para medição e identificar o critério mais adequado para a modelagem do volume de árvore individual. Os dados foram coletados em povoamentos de eucalipto com idade entre 58 e 65 meses. O modelo de Schumacher-Hall foi aplicado em cinco critérios de amostragem, com nove variações (45 no total): 1) número de árvores por classe diamétrica, sendo (a) número fixo, (b) proporcional à distribuição do diâmetro amostral, ou (c) proporcional ao desvio padrão da amostra; 2) tamanho da amplitude da classe diamétrica, que variou de 1,0 a 5,0 cm. As equações geradas em cada critério foram usadas para estimar o volume de fuste de árvores reservadas para validação. Isso permitiu calcular erros padrões da estimativa para esse conjunto de dados. Além disso, os resíduos das estimativas de volume foram examinados por meio de testes estatísticos para viés, autocorrelação e heteroscedasticidade. Os resultados mostraram melhores performances de equações de volume usando menores amplitudes. Não houve uma clara tendência em aumentar/reduzir a autocorrelação e/ou heteroscedasticidade dos resíduos. Aquelas amostragens com proporção à frequência da classe diamétrica apresentaram as melhores performances, inclusive usando apenas 36 árvores. Aquelas cuja escolha de árvores foi proporcional ao desvio padrão tiveram os piores resultados. Como conclusão, a seleção proporcional à frequência da classe diamétrica, sob condição de amostrar pelo menos duas árvores por classe, fornece modelos estatisticamente superiores aos demais quanto aos critérios sugeridos no estudo.
We examined the financial efficiency and effectiveness of landscape versus community protection fuel treatments to reduce structure exposure and loss to wildfire on a large fire-prone area of central ...Idaho (USA). The study area contained 63,707 structures distributed in 20 rural communities and resorts, encompassing 13,804 km2. We used simulation modeling to estimate expected structure loss based on burn probability and characteristics of the home ignition zone. We then designed three fuel management strategies that targeted treatments to: 1) the surrounding areas predicted to be the source of exposure to communities from large fires, 2) the home ignition zone, and 3) a combination of the landscape and home ignition zone. We evaluated each treatment scenario in terms of exposure and expected structure loss compared to a no-treatment scenario. The potential revenue from wood products was estimated for each scenario to assess the cost-efficiency. We found that the combined landscape and home ignition zone treatment scenario which treated 5.7% of the study area resulted in the highest overall reduction in predicted exposure (47.5%, 100 structures yr−1) and predicted loss (69.1%, 57 structures yr−1). Home ignition zone treatments provided the best predicted economic and per area treated performance where exposure and loss were reduced by one structure by treating 89 and 111 ha per year, respectively, with an annual cost of $33,645 and $73,672. Revenue from thinning was the highest for landscape fuel treatments and covered 16% of the required investment. This work highlighted economic and risk tradeoffs associated with alternative fuel treatment strategies to protect developed areas from large wildland fires.
•Home ignition zone treatments are considered most effective.•By contrast, forest landscape treatments can generate revenue.•Combining the strategies was predicted to have the highest exposure reduction.•Interactions between drivers of fire and structure loss created scale tradeoffs.•Local and multiscale treatment strategies are needed to address WUI fire risk.
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