No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Optimal Stocking Levels and Rotation Under Risk
Abstract
The usual joint optimization of stocking levels and rotation length discussed under the deterministic assumption is generalized to probabilistic cases. A probabilistic dynamic programming model is constructed to resolve the difficulties introduced. Every value in the deterministic model is replaced by an expected value in the probabilistic model, and the objective is to optimize the expected value. An example showing how to use the developed model to solve the optimal stocking levels and rotation problems under probabilistic growth for Douglas-fir is presented. The effects of various degrees of indeterminateness, or risk in growth prediction, are that for larger variance of growth prediction, optimal regimes involve shorter rotation, lower stocking levels and lower mean annual increment. Forest Sci. 28:711-719.
... During the past few decades substantial effort has been devoted to develop operations research techniques to optimize even-aged stand management (e.g., Brodie and Kao 1979, Kao 1982, Hoganson and Rose 1984, Buongiorno and Gilless 1987, Roise 1986, Pukkala and Miina 1997. Initially, the aim of most efforts was to schedule harvests to optimize stocking control without paying attention to risk. ...
... Initially, the aim of most efforts was to schedule harvests to optimize stocking control without paying attention to risk. Several authors have proposed dynamic programming (DP) models to optimize thinning regimes and rotation lengths (e.g., Amidon and Akin 1968, Brodie et al. 1978, Kao 1982, Buongiorno and Gilless 1987, Arthaud and Pelkki 1996. Hoganson and Rose (1984) also used DP to find optimal stand-level prescriptions within a forestwide lagrangian relaxation approach. ...
This article presents and discusses research with the aim of developing a stand-level management scheduling model for short-rotation coppice systems that may take into account the risk of wildfire. The use of the coppice regeneration method requires the definition of both the optimal harvest age in each cycle and the optimal number of coppice cycles within a full rotation. The scheduling of other forest operations such as stool thinning and fuel treatments (e.g., shrub removals) must be further addressed. In this article, a stochastic dynamic programming approach is developed to determine the policy (e.g., fuel treatment, stool thinning, coppice cycles, and rotation length) that maximizes expected net revenues. Stochastic dynamic programming stages are defined by the number of harvests, and state variables correspond to the number of years since the stand was planted. Wildfire occurrence and damage probabilities are introduced in the model to analyze the impact of the wildfire risk on the optimal stand management schedule policy. For that purpose, alternative wildfire occurrence and postfire mortality scenarios were considered at each stage. A typical Eucalyptus globulus Labill. stand in Central Portugal was used as a test case. Results suggest that the proposed approach may help integrate wildfire risk in short-rotation coppice systems management scheduling. They confirm that the maximum expected discounted revenue decreases with and is very sensitive to the discount rate and further suggest that the number of cycles within a full rotation is not sensitive to wildfire risk. Nevertheless, the expected rotation length decreases when wildfire risk is considered.
... Studies on forest planning under risk have, to some extent, focused on economic parameters such as stochastic timber prices and harvesting costs. Studies on planning under risk in the growth process are not as common, although many articles treat the problem (e.g., Kao 1982, Hof et al. 1988, Gove and Fairweather 1992, Valsta 1992, Pukkala and Miina 1997, Kangas and Kangas 1999. ...
... Hof et al. (1988) and Pickens and Dress (1988) introduced random components in an LPformulation. A common approach for restricted problems is to use stochastic dynamic programming (e.g., Riiters et al. 1982, Kao 1982, Haight 1990), a technique which provides an opportunity for decisions to be made adaptively based on the outcome of the random process. A problem is, however, that the outcome must be observed. ...
Nyström, K. & Ståhl, G. 2001. Forecasting probability distributions of forest yield allowing for a Bayesian approach to management planning. Silva Fennica 35(2): 185–201. Probability distributions of stand basal area were predicted and evaluated in young mixed stands of Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) Karst.) and birch (Betula pendula Roth and Betula pubescens Ehrh.) in Sweden. Based on an extensive survey of young stands, individual tree basal area growth models were estimated using a mixed model approach to account for dependencies in data and derive the variance/covariance components needed. While most of the stands were reinventoried only once, a subset of the stands was revisited a second time. This subset was used to evaluate the accuracy of the predicted stand basal area distributions. Predicting distributions of forest yield, rather than point estimates, allows for a Bayesian approach to planning and decisions can be made with due regard to the quality of the information.
... Зокрема, С.Ганн розглядає проблему ієрархічного планування лісового менеджменту, приділяючи осо-бливу увагу моделям тактичних рівнів [197]. Розглядаючи проблему стосовно стохастичного програмування, К.Као висловлює своє розуміння достовірності даних і значення процесу планування [212]. ...
Розглянуто теорію та практику сталого лісокористування: поняття і принципи сталого лісокористування, сутність поняття «сталі екосистеми», системний підхід до менеджменту екосистем, еколого-економічну ефективність багатоцільового використання лісових ресурсів, урахування фактора часу і невизначеності в процесі оцінювання послуг лісових екосистем, еколого-економічні особливості лісокористування у гірських районах Карпат. При розгляді методів оптимізації комплексного лісокористування досліджено об'єкти та критерії оптимізації лісокористування, роль економіко-математичного моделювання в оптимізації лісо-
користування, економічну оцінку лісових ресурсів, методи багатокритеріальної оптимізації, принципи лісового менеджменту, фактори впливу на еколого-економічну ефективність лісокористування, функції потенціалу лісових ресурсів, оптимізацію лісокористування на основі вибору альтернативних варіантів, інтегральний еколого-економічний ефект багатоцільового лісокористування. Прикладні аспекти оптимізації лісокористування розкриваються в оптимізації обороту рубки на основі вибору альтернативних варіантів, розрахунку еколого-економічної ефективності лісокористування в гірських умовах Карпат, застосуванні методу Фаустмана для еколого-економічної оцінки лісокористування, еколого-економічної оцінки заходів щодо покращення стану зелених насаджень міст.
... In contrast we only focus on studies based on Markov chains in order to describe the similarities and differences with our study. Since forest management can be modeled as a controlled Markov process ( Lohmander, 2011), the Markov decision process 1 is a technique commonly used to deal with risk and uncertainty at the stand level ( Hool, 1966;Lembersky and Johnson, 1975;Kao, 1982;Teeter and Caulfield, 1991;Pastor et al., 2005;Lin and Buongiorno, 1998;Kaya and Buongiorno, 1987;Rollin et al., 2005;Buongiorno and Zhou, 2011;Zhou and Buongiorno, 2011) as well as at the forest level when addressing spatial problems ( Spring et al., 2005a;Sabbadin et al., 2007;Forsell et al., 2011). However, the current literature concerning the MDP model only considers risk-neutral forest owners. ...
Forests are increasingly threatened by windthrows but those composed of uneven-aged stand plots are generally less impacted by their effects. As a consequence, the management of such forests should be based on a joint management of all their different uneven-aged stand plots. This article determines the optimal management regime of uneven-aged forests under risk of windthrow and furthermore takes the risk preferences of the forest owner into account. This study analyzes optimal harvesting of uneven-aged stand plots by applying a Markov decision process (MDP) framework using an economic description of uneven-aged forestry. Two management types are considered: the joint uneven-aged forest management model in which the forest owner jointly manages all the different stand plots, and the independent uneven-aged forest management model that assumes that the forest owner independently manages each plot of the forest. The MDP framework is applied to a non-industrial private forest owner located in northeastern France. First, we show that the forest owner tends to converge toward a forest structure that is close to a normal forest in the joint uneven-aged forest management model. Second, we find that the independent uneven-aged forest management model poorly approximates the optimal multi-stand harvesting policy. Third, and more surprisingly, the levels of windthrow probability changes considered have little influence on the optimal harvesting strategies of the forest owner. Lastly, in contrast, the forest owner's risk aversion is shown to have a strong influence on the optimal policy.
... This explosion of R&U papers in forestry economics since the late 1980's is noteworthy because before this time there were only a handful of papers addressing a range of R&U issues. An incomplete list of earlier papers includes: Norstrom (1976) and Voltaire (1980 &1983), which addressed determination of optimal harvest age with stochastic prices; Routledge (1980) and Reed (1984) which assessed fire risk; Mills and Hoover (1982), which compared the magnitude and timing of forest returns with non-forest assets; and Kao (1982 and, which focused on the computational aspects of finding solutions. 3 The more than 30 R&U papers published since 1988 not only explore the research areas developed in these earlier R&U papers, but develop several new areas. ...
... There are many examples of the integration of risk in stand-level optimization (e.g., Kao, 1982;Caul®eld, 1988;Valsta, 1992) and forest-level analysis (e.g., Dixon and Howitt, 1980;Law and Kelton, 1982;Hoganson and Rose, 1987;Gong, 1994;Boychuck and Martell, 1996;Forboseh and Pickens, 1996). However, there are only a few examples of multiobjective forest-wide planning with multiple sources of risk although multiple objectives and multiple risks characterize most planning situations. ...
Multiple risks were integrated in multi-objective forest planning with the scenario technique and with an application of multi-attribute utility theory. The sources of risks were divided into three categories: risks related to inventory data, risks arising from unknown future states of nature, and risks associated with the decision maker's preferences. Stochastic models and other procedures for producing scenarios of inventory data, growth rate, mortality and natural regeneration of trees, success of tree planting, timber prices, cost level, and importance of management objectives are described. Some of the models for the scenarios were based on empirical data and obtained from earlier investigations, while others were specified by parameters given by the decision maker. The decision maker's attitude toward risk was integrated in planning via the distribution of a utility index. The utility index was computed from an additive utility function. Cumulative points of the distribution were weighed in a manner reflecting decision maker's risk preferences. The weighed utility index was used as the ultimate criterion when searching for the optimal plan. Optimization was done using a heuristic algorithm. The case study conducted indicated that both risks and attitude toward risks affect the choice of plan; optimal plans produced by a deterministic system were different from the stochastic optima, and a risk-neutral decision maker had optima different from those of risk-averse and risk-seeking decision makers. Depending on the decision maker's attitude toward risk, utility losses ranging from 0.1% to 4.5% were to be expected when the deterministic optimum was selected. Implementing a risk-neutral decision maker's optimal plan caused utility losses less than 3.5% for risk-averse and risk-seeking decision makers.
... Existen numerosos artículos que abordan la fuente del riesgo en la actividad forestal, especialmente relacionado con fuego, daño por insectos y económico. Básicamente, los autores usan como método analítico modelos de decisión de Markov, programación dinámica, árboles de decisión y simulación de Monte Carlo, entre otros (Kao 1982, Washburn y Binkley 1990b, Haight 1991, Reed y Apaloo 1991, Newman y Williams 1991, Taylor y Fortson 1991, Teeter y Caulfield 1991, Pukkala y Kangas 1996, Reed y Haight 1996, Brazee y Bulte 2000. ...
The determination of optimum silvicultural regimes has been based traditionally on the assumption that all results from management activities are without risk. Decision strategies in forest management must be based on a solid knowledge of the cause and effect relationships between silvicultural requirements and financial dynamics. In this paper, the relevant literature is reviewed in order to incorporate risk analysis into both silvicultural investment and forest management.
... Dynamic programming techniques have also been employed in some of the first studies related to risk of fire (Martell, 1980) in a deterministic way. In this study stochastic dynamic programming was used to deal with risk when finding optimal management alternatives to optimize stocking level and rotation length: Kao (1982) presented a study dealing with uncertainty in growth predictions due to fire occurrence or storms where they used fixed probabilities of occurrence. This model would be applicable for these risk factors if the probabilities of their occurrence and the associated growth are known. ...
Since forest planning is characterized by long time horizons and it typically involves large areas
of land and numerous stakeholders, uncertainty and risk should be taken into account when
developing forest management plans. There are many sources of uncertainty and risk, e.g.
regarding the future states of nature, future market conditions, occurrence of catastrophic
events, errors in forest inventory and performance of the models employed by the managers or
preferences of the decision maker(s). These sources of risk and uncertainty have been
commonly ignored due to the lack of both information about the uncertainties and the required
tools to integrate them in the planning process, leading to the adoption of suboptimal or even
bad alternatives. Nevertheless, different techniques have been used to deal with risk and
uncertainty in forest planning.. The aim of this study is to review different methods to deal with
risk and uncertainty in forest planning, listing problems that forest managers may face during
the preparation of management plans, and trying to serve as a guide for the application of each
method according to the problem case. Moreover, innovative approaches are introduced
howing the opportunities that their application presents in forest planning.
... The first application of MDP models to forestry was proposed by Hool [17], and the first practical application was carried out by Lembersky and Johnson [21], who studied the optimum management of a stand with growth and price risks. Similar studies have followed, e.g., Kao [18], Teeter and Caulfield [36] and Pastor et al. [27]. Other studies have extended this approach to include ecological criteria (Lin and Buongiorno [22]), uneven-aged forest management (Kaya and Buongiorno [19]) or both (Rollin et al. [32]), as well as stochastic interest rates (Buongiorno and Zhou [7]; Zhou and Buongiorno [37]). ...
Windstorms generate windfalls that may lead to price decreases. Studies have often focused on stochastic growth and price, but considered that the link between these two risks was generally nil. In our model, we assume that storms generate windfalls and that these windfalls have an impact on timber price through volume and quality. The objective of this paper was to analyze the impact of these two effects on harvesting behavior. We considered that timber stock follows a Markov Decision Process (MDP) and that the harvesting decision is a control variable. We solved the optimal harvesting problem under storm risk with a risk-averse forest owner and when the storm has an impact on production and price. We studied the impact of a change in the storm risk distribution, the percentage of quality loss and risk aversion on the optimal harvesting decision.
... Expected values for LEV, NPV and NPV inc were obtained. The simulation procedure used was Monte Carlo, which involves totally random sampling; 50 simulations with 1 500 iterations were performed in order to obtain the probability of financial results (Kao 1982 ...
The Loblolly pine (Pinus taeda L.) plantation area in north-east Uruguay was 108 000 ha in 2008. Recent industrial capacity developments have resulted in major structural changes. Silvicultural system selection depends on site productivity, costs, timber prices and public policies. This study aimed to assess economic returns for two silvicultural systems in north-east Uruguay, in scenarios with and without a plantation subsidy: System I, with a short, 12-year rotation, primarily for small logs; and System II, with a longer, 24-year rotation. For System I, the underbark volume was 198 m3 ha−1 (mean annual increment16.5 m3 ha−1 y−1) and land expectation value (LEV) at a 9.7% discount rate was US442 ha−1, with and without subsidy, respectively. System II resulted in 318 m3 ha−1 underbark volume (13.2 m3 ha−1 y−1) and the LEV was US771 ha−1, with and without subsidy, respectively. System I was more profitable than extensive cattle husbandry only when the distance to mill was equal to or less than 60 km and wood millyard prices were equal to or higher than US28.8 m−3 with and without subsidy, respectively. Values for System II, in which the main product was a mix of sawlog diameters, were positive and higher than those for System I, both with and without subsidy. If a company invested in forest plantations without due provision for early silvicultural treatments, such as pruning and precommercial thinning, a high risk of financial loss would ensue. Long-rotation sawtimber regimes similar to System II would be more profitable and offer a lower risk of financial losses. The results suggest subsidy withdrawal in Uruguay should not lead to changes in silvicultural systems; in fact, it rendered regimes designed for low-value wood, such as System I, even less advisable.
... However, it may be noted that if there are many stochastic factors, MDP models (or simulation, discussed below) may be the only computationally feasible option. Examples of MDP models are numerous and include Lembersky and Johnson, Norstrom [40], Kao [26], Teeter and Caulfield [52], and Kaya and Buongiorno [29], Lin and Buongiorno [32] and Buongiorno [9]. Lin and Buongiorno incorporate natural catastrophes, as well as diversity of tree species and tree size. ...
This paper develops a two factor real options model of the harvesting decision over infinite rotations with mean reverting stochastic prices using a rigorous Hamilton-Jacobi-Bellman methodology. The harvesting problem is formulated as a Linear Com-plementarity Problem which is solved numerically using a fully implicit finite difference method. This approach is contrasted with Markov Decision Process models commonly used in the literature. The model is used to examine a proposed investment in intensive forest management in Ontario's boreal forests. The value of a representative stand in the Romeo Malette forest is estimated assuming complete harvesting flexibility. This is contrasted with the value of the stand when regulations dictate a window of time during which harvesting must occur. The authors acknowledge with gratitude the financial support of the Living Legacy Trust in Ontario, Tembec Inc., the Agricultural Research Institute of Ontario, the Upper Great Lakes Environmental Research Network, and the Ministry of Natural Resources of Ontario. The opinions expressed herein represent the views of the authors, and not of the agencies that provided financial support. The authors would also like to thank numerous individuals who provided useful information and com-ments. These include Margaret Penner (Forest Analysis Ltd.), George Bruemmer, Al Stinson and Paul Krabbe (Tembec), Wayne Bell (Ontario Ministry of Natural Resources), Glenn Fox (University of Guelph), and Peter Forsyth (University of Waterloo). Any shortcomings or errors are solely the responsibility of the authors.
... The optimization of even-aged stand management planning has been addressed by several authors (e.g. Brodie and Kao 1979; Kao and Brodie 1979; Kao 1982: Buongiorno and Gilless 1987; Roise 1986; Pukkala and Miina 1997). The reader is referred to Valsta (1990) and Hyytiäinen (2003) for comprehensive reviews of numerical methods for the optimization of even-aged stand management. ...
Maritime pine (Pinus pinaster Ait) is a very important forest species in Portugal. Nevertheless, both revenues and timber flows from the pine forests are substantially impacted by forest fires. We present a methodology for integrating fire risk in Maritime pine stand-level management optimization in Portugal. The objective is to determine the optimal prescription for a stand where fire risk is related to its structure and fuel load. The study optimizes the thinning treatments and the rotation length, as well as the fuel treatment schedule, i.e., reduction of understory cover during the rotation. Two components of wildfire risk—occurrence and damage—are considered. Fire damage was treated as an endogenous factor depending on the stand management schedule while fire occurrence was considered exogenous. Apreliminary model that relates the expected loss to stand basal area, mean tree diameter and fire severity was used for this purpose. The article demonstrates how a deterministic stand-level growth and yield model may be combined with wildfire occurrence and damage models to optimize stand management. The Hooke-Jeeves direct search method was used to find the optimal prescription. In addition, population-based direct search methods (e.g. differential evolution and
particle swarm optimization) were used for further testing purposes. Results are presented for Maritime pine stand management in Leiria National Forest in Portugal. They confirm that fuel treatments improve profitability and reduce the expected damage.
KeywordsOptimization–Simulation-optimization system–Forest planning–Wildfire risk–Fuel treatment–Pinus pinaster Ait
... Valsta (1992b) found that, with increasing stochastic growth variation, thinning is scheduled sooner and rotation length is increased. According to Kao (1982), the risk in growth prediction makes optimal rotations shorter and stocking levels lower. In our case, risk in growth and price decreased the optimal post-thinning stand density but increased the rotation length. ...
The paper describes a way of simultaneously optimizing several stand management objectives differing in measurement units and character. The simulation-optimization system accommodates, besides multiple objectives, the time and risk preferences of the decision maker. Multiple objectives are integrated in optimization through an additive utility function. Time preferences are dealt with by discounting, and the discounting rate is specified separately for each objective. Objectives related to products are described by the sum of the discounted values while objectives related to the status of the forest are described by the integral of the discounted value of a state variable. Different units are made commensurable via subutility functions that scale all objective variables between zero and one. Risks associated with the future growth level and timber prices, and with the preferences of the decision maker, are taken into account by stochastic optimization based on the scenario technique. With this technique, each management alternative produces a distribution of utility indices. This distribution is used to compute a utility index corrected by risk preferences; different parts of the distribution are weighted in a manner that reflects the decision maker's attitude toward risk. A case simulation-optimization system is described, based on the above techniques, to deal with multiple objectives, time preferences, risks and risk preferences. Calculations using this system indicated that security and recreational amenities lengthen the optimal rotation of mixtures of Scots pine and Norway spruce, compared to a situation in which the maximal soil expectation value is the only objective. In a multiobjective case, stochastic growth, timber price and preferences increased the rotation length by 15 years (17%) from the deterministic optimum. Attitude toward risk also affected the optimal stand management.
... Lembersky and Johnson (1975) extended Hool's formulation by considering an infinite time horizon and by using additional state variables. Kao (1982) used a probabilistic DP model to jointly optimize stocking levels and tim ing of the final harvest. His model incorporated uncertainty in the prediction of growth and maxi mized a volumetric objective function. ...
This review describes the current state of the art of management science applications in forest land management and the forest products industry. The evolution of applications of management science to forestry problems is traced from the late 1950's to the present. While management science is extensively utilized in both the public and private sectors, many institutional and technical barriers exist to hinder an even wider acceptance. Reasons for this and possible ways to ameliorate these problems are presented.
... A few studies have incorporated thinning into stochastic decision making models for even - aged stand management under price risk . Using a forward recursive dynamic programming method , Kao ( 1982 , 1984 ) analyzed the optimal thinning and rotation problems under conditions of different degrees of knowledge of timber growth . Haight and Smith ( 1991 ) , and also Carlsson ( 1992 ) , used a stochastic dynamic programming method to optimize the thinning and final harvest of mixed - species stands . ...
Abstract
It is well known that decision making problem solving in forest management involves risks from different sources. In many cases, the incorporation of risk will change the optimal decisions in different ways. Usually, stochastic optimization models are much more complicated than the corresponding deterministic ones, and greater computational efforts are required for identification of the optimal solutions. Thus, simplification of the decision making problems is often made in one way or another, the cost being deviations from reality. In this thesis, a new optimization approach has been designed for decision problems concerning harvesting under price risk, both for single species stands (paper I) and for mixed species stands (paper II). The intention with this approach has been to keep the model simple with respect to the computational burden, without imposing very restrictive assumptions on the choice of feasible decision alternatives. Optimal stocking level functions, which are modeled as functions of stand age and stumpage price, are applied to guide the thinning decisions. A reservation price function, which is formulated using stand age and standing timber stock as independent variables, and market price observations are used to determine the final harvest time. The coefficients of these functions are calculated by simulation.
Flexibility is valuable in decision making under risk. Recently, the risk of damage to forests by moose in Sweden has been widely recognized. This problem will most likely exist also in the future, since moose hunting is very popular in the country. Study of this problem is highly relevant to forestry. In Paper III, the value of flexibility for a mixed species stand is analyzed when risks in timber price and moose damage are incorporated. An adaptive optimization model has been developed to determine the initial mix of species which maximizes the expected present value. The results show that mixed-species stands of Scots pine and Norway spruce are preferable to pure Scots pine stands when the risks of moose damage and timber price are taken into account.
The efficiency of the model also depends on the optimization technique applied. Paper IV works on a hybrid heuristic algorithm, based on a genetic algorithm and a traditional non-linear optimization method: the Hooke and Jeeves method. It is shown that the performance of the hybrid algorithm is significantly better than that of the Hooke and Jeeves method, and of the Powell search method.
... Previous research has applied a variety of methods to determine the optimal timing and intensity of thinnings and rotation age. Examples of the methods used in previous studies include marginal analysis (Chappelle and Nelson 1964), optimal control theory (Näslund 1969), inventory theory (Pelz 1977), dynamic programming (Amidon and Akin 1968, Brodie et al. 1978, Brodie and Kao 1979, Brodie and Haight 1985, nonlinear programming (Kao and Brodie 1980, Roise 1986, Solberg and Haight 1991, Valsta 1992, and stochastic dynamic programming (Lembersky and Johnson 1975, Kao 1982, 1984, Haight and Smith 1991, Carlsson 1992. Initially, an important objective of the research was to evaluate different optimization methods in order to improve the computational efficiency (e. g. ...
An integrated thinning and final harvesting strategy for even-aged stand under conditions of uncertainty in future timber prices is developed. This strategy consists of two parts: a feedback stocking-level control function that guides the choice of thinning intensities at different ages, and a reservation price function that determines the time of final harvesting. Optimal stocking level is modelled as a function of stand age and market timber prices. The reservation price function is formulated using stand age and standing timber stock as independent variables. The coefficients of the two functions are optimised simultaneously for a sample stand of Scots pine (Pinus Sylvestris L.) located in northern Sweden. The functions obtained are then used to simulate the thinning and final harvesting decisions for the sample stand. The integrated strategy is compared with a pure reservation price strategy where no thinning is allowed, and with an open-loop harvesting strategy that ignores timber price uncertainty.
Die Frage nach den optimalen Holznutzungsmengen in Wäldern ist für die Forstwirtschaft seit den Anfängen einer nachhaltigen Waldbewirtschaftung aktuell. In dieser Arbeit wird ein Modell aus der Ressourcenökonomie, einem Teilgebiet der Umweltökonomie, für die Nutzungsplanung in Wirtschaftswäldern eingesetzt. Bisher wurde dieses Modell nur bei anderen natürlichen Ressourcen für die Optimierung der Erntemengen angewendet. Das Modell wird für die Anwendung auf die Ressource Holz erweitert und anhand empirischer Daten aus dem bayerischen Staatswald auf seine Eignung für die Forstwirtschaft geprüft. Es erweist sich dabei vor allem für die langfristige Forstbetriebsplanung als ein geeignetes Instrument, um Entscheidungen auf Betriebsebene über die Vorratshaltung und die Nutzungsmengen zu unterstützen.
In the forest the silvicultural and utilization process is carried out by performing a sequence of decisions, like the felling and the planting of the trees. Within these practices the forest product is yielded. The amount of the yield should stay at an approximately fixed annual level. This could be realized by so-called “normal forest”. Moreover, living and growing of the trees are affected by unpredictable natural circumstances. Therefore, the forest as a system contains both, the decision making and the probabilistic features. Stochastic dynamic models are very appropriate for providing the optimal forest management decisions maximizing the sustained timber production and net revenues to the society (Hool (1966), Lembersky et al. (1975), Binkley (1980), Kao (1982), Kaya et al. (1987), Hassler et al. (1988)).
If land has been assigned indefinitely to timber production, the age at which trees should be clearcut and the land replanted must be determined. This is an optimal replacement problem, similar to that encountered in livestock management. However, just as in the production of livestock for meat, there may be other management decisions taken between replacement decisions which affect final biomass at replacement. In the case of livestock production the decisions are usually feed input decisions, whereas in the case of timber production the decisions are output decisions on partial harvesting before clearcutting.
Compared to other production systems, forests are characterized by the long-term of its outcomes (e.g. rotation lengths are high). In this system the state of nature that would prevail after such long periods is not known with certainty. The consequences of a decision depend on many uncontrollable variables which in turn determine the outcome of the decision. Uncertainty and risk are thus closely related to the development of forest management plans.
Forest planning is ineffective if it ignores these sources of uncertainty and risk. The main reason is that projections of forest conditions and outcomes done during the planning process may be very different if they include risk. This is especially important in industrial plantations where the decisions rely on forest productivity predictions.
The variety of planning models is great, but applications of risk analysis are not very common in forest planning (Pasalodos-Tato M, Makinen A, Garcia-Gonzalo J, Borges JG, Lämas T, Eriksson O, For Syst 22(2):282–230, 2013. http:// dx. doi. org/ 10. 5424/ fs/ 2013222-3063). This chapter explains the concept of risk and uncertainty. It further explains and presents examples on how to integrate them in forest planning. For a more complete review the readers are referred to Yousefpour R, Thorsen BJ, Jacobsen JB, Meilby H (Ann Forest Sci 69:1–15, 2012) and Pasalodos-Tato M, Makinen A, Garcia-Gonzalo J, Borges JG, Lämas T, Eriksson O (For Syst 22(2):282–230, 2013. http:// dx. doi. org/ 10. 5424/ fs/ 2013222-3063).
Since 1981, U.S. institutional investors have placed $5.8 billion into timberland assets. They include timberland in their portfolios because returns have competed strongly with traditional portfolio assets, are perceived as low risk, and return correlations with other portfolio assets are low. The subject of timberland returns and risk should therefore be of practical interest to timberland investment management companies (TIMCOs), the firms that manage these assets for institutions. To date, however, the application of academic research on risk to operational timberland investment problems is limited. This paper discusses which research is employed by TIMCOs, which is not, and suggests reasons why.
A survey of optimal timber harvesting models is presented. Even-aged and uneven-aged, single-stand models, and forest-level scheduling models are considered.
In recent years, the applications of dynamic optimization procedures in natural resource management have proliferated. A systematic review of these applications is given in terms of a number of optimization methodologies and natural resource systems. Optimization methods are characterized by (1) the mathematical model used to describe a natural resource system, (2) a set of feasible strategies available to the resource manager, and (3) an objective functional by which to measure benefits and costs of strategies. A formal statement of the control problem is used to describe six approaches to optimal utilization of renewable natural resources: variational mathematics, specifically Pontryagin's Maximum Principle; dynamic programming; linear programming; nonlinear programming; simulation-optimization; and classical procedures. Solution methodologies are illustrated for each of these approaches, and examples from the ecological and natural resource literature are described for various subject matter areas. Applications are highlighted in terms of model structures, objective functionals, and system constraints. To the extent possible, optimal management patterns are characterized. Finally, the applicability of the methods to renewable natural resource systems are compared in terms of system complexity, system size, and precision of the optimal solutions. Recommendations are made concerning the appropriate methods for certain kinds of biological resource problems.
A forest-management area which has to be managed in given natural circumstances with certain economic and environmental aims is presented through a dynamic model. In order to develop and manage a model, this article deals with strategies of forest management which result in maximal sustained financial yield. Since the process that directs the development of the forest management area is long-term and consists of several stages, the structure of the model has been created using a discrete dynamic programming, based upon Bellman's principle. The model presented was tested on a small and simplified example of the forest management area. The obtained results confirm that the model could be of practical use and easily extended by introducing more complexity into it.
Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The objective function is then the expected discounted value of returns, over an infinite horizon. It gives the land or the forest value in a stochastic environment. In MDP models, the laws of motion between stand-price states are Markov chains. Faustmann's formula is a special case where the probability of movement from one state to another is equal to unity. MDP models apply whether the stand state is bare land, or any state with trees, be it even- or uneven-aged. Decisions change the transition probabilities between stand states through silvicultural interventions. Decisions that maximize land or forest value depend only on the stand-price state, independently of how it was reached. Furthermore, to each stand-price state corresponds one single best decision. The solution of the MDP gives simultaneously the best decision for each state, and the forest value (land plus trees), given the stand state and following the best policy. Numerical solutions use either successive approximation, or linear programming. Examples with deterministic and stochastic cases show in particular the convergence of the MDP model to Faustmann's formula when the future is assumed known with certainty. In this deterministic environment, Faustmann's rule is independent of the distribution of stands in the forest. FOR. SCI. 47(4):466474.
Simulation was used to predict seed yields for loblolly pine seed orchards in the Western Gulf Region of the United States. This approach allows a seed orchard manager to incorporate site-specific information as well as estimates about the effects of alternative management plans on predicted seed yields. Furthermore, the risks associated with different alternatives can be evaluated by calculating confidence limits for predicted yields. The utility of the simulation approach was demonstrated by comparing alternatives that assumed reduced yield variability, shortened orchard rotations, and reduced age to first seed production. South. J. Appl. For. 23(2):117-123.
In this paper, a discussion of the development of the optimal forest rotation literature and an extensive bibliography is presented. The body of literature has grown at an almost constant rate for the past two decades, with no apparent let-up likely. A total of 313 published works have appeared in books and over sixty journals, with individuals contributing to this body of work. Developed from the relatively simple question of the determination of the value of timberland, the optimal rotation literature has grown into a mature discussion that embodies a full range of issues and topics.
Markov decision process (MDP) models generalize Faustmann's formula by recognizing that future stand states, prices, and interest rates, are not known exactly. Buongiorno (Forest Science 47(4) 2001) presents a dynamic programming and a linear programming formulation of the MDP model with a fixed interest rate. Both formulations are generalized here to account for a stochastic interest rate. The objective function is the expected present value of returns over an infinite horizon. It gives, like Faustmann's formula, the value of the land and the eventual standing trees. The changes between stand states, prices, and interest rate, are represented by Markov chains. Faustmann's formula is a special case where the change from one state to another has 0 or 1 probability, and the interest rate is constant. The MDP model applies to any stand state, even- or uneven-aged, and the best decisions are tied uniquely to the current system state. An example shows the effects of recognizing variations in interest rate on the land expectation value, and the cost of ignoring them.
Determination of optimal forest-management regimes has been traditionally based on the assumption that the outcome of the management activity is certain. This was the case despite the almost universal recognition that forest-management outcomes are, in fact, uncertain. In this paper, a comprehensive conceptual framework for incorporating risk in forest-management and silviculture investment is developed. The framework distinguishes between decision problems which are structured and those which are unstructured. For the former, the framework focuses upon achieving a match between the decision-problem representation and the degree of knowledge of risk preferences, risk-preference structures and the nature of the risks. For unstructured decisions a new formulation based upon the concept of resilience is developed. The two framework are reconciled through a calculus of risks, benefits and resilience.
This paper presents an integrated strategy for thinning and final harvest decisions in even-aged stand management under conditions of uncertainty in future timber prices. The strategy consists of two parts: an optimal stocking level function that guides the choice of thinning intensity, and a reservation price function for determining the time of final harvest. Optimal stocking level is modelled as a function of stand age and stumpage price. The reservation price function is formulated using stand age and standing timber stock as independent variables. The coefficients of the two functions are optimised simultaneously for an example stand of Scots pine (Pinus Sylvestris L.) in northern Sweden. The functions obtained are then used to simulate the thinning and final harvest decisions for the example stand. The integrated strategy is compared with a pure reservation price strategy where no thinning is allowed, and with the optimal management regime determined based on the expected timber prices.
The paper considers a forest management problem, which consists of decisions on investment, silvicultural and harvesting activities for an existing forestland over a long time horizon,while guaranteeing sustainability,maximizing the expected profit, referring to ecological objectives and the public’s acceptance of decisions. In order to solve this problem, several decision support systems and models were developed. Here, we present a fuzzy, dynamic and multi-objective model for optimal forest management, which determines the sequence of decisions that jointly maximizes economic, ecological and social objectives, respects prescribed constraints and imprecision, and takes the forest system from its existing state to the goal state. The idea of fuzzy analytic hierarchy process is introduced within a discrete dynamic programming process to evaluate the conflicting objectives. The cumulative impacts of objectives are formulated on the basis of attributes as a sum over all products of their membership functions and their relative importance (weights). Finally, the problem is presented in a form of a network, and the optimal policy over all time periods is determined using the iteration method for the solution of sequential decision processes of Bellman’s type. A case study involving the forest Panovec, Slovenia is used to demonstrate the application of the presented model
Diss. -- Helsingin yliopisto.
This article develops a two-factor real options model of the harvesting decision over infinite rotations assuming a known
stochastic price process and using a rigorous Hamilton-Jacobi-Bellman methodology. The harvesting problem is formulated as
a linear complementarity problem that is solved numerically using a fully implicit finite difference method. This approach
is contrasted with the Markov decision process models commonly used in the literature. The model is used to estimate the value
of a representative stand in Ontario's boreal forest, both when there is complete flexibility regarding harvesting time and
when regulations dictate the harvesting date.
A method is presented for determining optimal economic strategies for density management in loblolly pine stands in the southern United States. A stochastic dynamic programming model employs a price state transition matrix constructed using time-series data for National Forest pine stumpage in the South. The model also incorporates WTHIN, a pine growth and yield simulator widely used in the South to support economic analyses of stand management alternatives. Results indicate that optimal net present values associated with management strategies determined for the stochastic model (relative to a deterministic equivalent) are higher due to differences in the thinning and final harvest decisions recommended by the two models.
ResearchGate has not been able to resolve any references for this publication.