Atsushi Yoshimoto

Searching for an optimal rotation age for forest stand management under stochastic log prices

Due to rapid change in timber prices in the Japanese market most likely affected by imported timber from countries such as the U.S., Canada, and the Nordic countries, the domestic forest managers have been facing a large degree of future price uncertainty. Because of this, it becomes necessary to take the future price uncertainty into account within the forest management framework. In this paper, the continuous time stochastic process, i.e., the geometric Brownian motion, has been used to model the log price process. The binomial option pricing approximation was then applied to value the Sugi (Cryptomeria japonica) and Hinoki (Chamaecyparis obtusa) forested land under stochastic log prices in order to search for an optimal rotation age. Our experiments with the proposed two state stochastic dynamic programming model showed that when the current log price is high enough to cover all costs, an optimal rotation age from the stochastic price and deterministic price models coincides, although the total expected present net value from management activities differs. Also it was shown that as the current log price decreases, an optimal rotation age derived from the stochastic price model becomes longer than that from the deterministic price model. If the current log price further decreases, then forest management will be abandoned, and the forest stand will be converted into alternative uses.

Potential Use of a Spatially Constrained Harvest Scheduling Model for Biodiversity Concerns: Exclusion Periods to Create Heterogeneity in Forest Structure

The objective of this paper is to investigate potential use of a spatially constrained harvest scheduling model for biodiversity concerns. Change in the degree of biodiversity is represented only by spatial characteristics of harvesting patterns of forest stands with different exclusion periods applied to adjacent forest stands. A spatially constrained harvest scheduling model called SSMART (Scheduling System of Management Alternatives foR Timber-harvest) is used for the analysis. It is one of the heuristics to solve a spatially constrained harvest scheduling problem by using the partitioning heuristic. The algorithm incorporated into SSMART is designed to seek a solution for a multicriteria problem with present net value maximum, meeting spatial feasibility and minimizing period-to-period harvest flow fluctuation, approximating even-flow constraints within the 0–1 integer programming framework. Our experimental analysis shows that the longer exclusion period, the less the harvest flow level and the total present net value are derived and the more heterogeneous the forest structure becomes in terms of the forest stand age distribution. It is also shown that the three exclusion period results in a stable forest stand age distribution over the time horizon for our experimental forest.

Stochastic control modeling for forest stand management under uncertain price dynamics through geometric brownian motion

In this paper, a stochastic control model is constructed by incorporating geometric Brownian motion to capture uncertain price dynamics into a one-stage and two-state stochastic dynamic programming model. The proposed model is designed to search for optimal harvest timing under price uncertainty without considering other forestry operations,e.g., thinning. We consider the option of abandoning forest management for an alternative use of forest land besides replantation. Our experimental analysis shows that the optimal harvest timing under stochastic log prices is delayed when a price level is crucially low for maintaining the management. It is also shown that when the current log price is sufficiently high, the optimal harvest timing derived from both the stochastic and deterministic approach becomes the same. With a downward trend of stochastic price dynamics, the optimal harvest timing tends to be hastened overall. This is because of the depreciation effect on the future return, which stimulates harvesting in an earlier period.

Stand-Level Forest Management Planning Approaches

Seeking an optimal operational regime under different management environments has been one of the main concerns of forest managers. Traditionally, the main operational regime includes planting density or regeneration scheme, thinning time/intensity, and optimal time to harvest over the given time horizon. Deterministic approaches to tackle this type of optimization problem with different controls have dominated the solution techniques in forestry literature. We present in this paper an overview of the methodologies used in stand-level optimization, in which we show the strengths and weaknesses of these methodologies as well as provide comments on the effectiveness of the methodology. We then propose a new dynamic programing approach for generalizing solution specification and techniques.

Threshold price as an economic indicator for sustainable forest management under stochastic log price

We seek the minimum harvest age and threshold price for sustaining forest management by constructing a stochastic dynamic programming model using a geometric mean-reverting process for log price dynamics. Three decisions—“Wait for harvest”, “Harvest & Plant”, and “Harvest & Abandon”—are assumed. The applied growth simulator is deterministic. Using the monthly time series data of sugi (Cryptomeria japonica) log price from 1975 to 2006, our analyses show that when the reverted mean is lower than the cost, the minimum harvest age increases as the current price approaches the threshold price, then declines. In other cases with a higher reverted mean, the minimum harvest age increases as the current or initial log price decreases. When the initial log price approaches the threshold price, the minimum harvest age tends to increase. These phenomena can be used to evaluate the possibility of management abandonment under a stochastic situation of log price dynamics.

Risk Analysis in the Context of Timber Harvest Planning

Events related to forest management are associated with uncertainty. This affects the management decision for forest level planning as well as stand level planning. In this paper, two stochastic models are introduced. The first model is a macro-type stochastic model for timber supply analysis by predicting harvesting events over the time horizon, while the second model is a micro-type stochastic model used to search for an optimal rotation for forest stand management under price uncertainty. A macro-type approach describes private forest owners’ harvesting behavior with the use of a stochastic process. The threshold method was assumed for the decision-making mechanism. In contrast, a micro-type approach was to search for an optimal rotation period for forest stand management under price uncertainty. Unlike the macro type approach, uncertainty was assumed for log price, which affects an optimal decision for the stand management. Stochastic differential equations are applied to capture stochasticity of price dynamics, and a stochastic dynamic programming approach is utilized for optimization. The continuous time stochastic process, i.e. the geometric Brownian motion, is used to model the log price process. The binomial option pricing approximation is then applied to discretize the price dynamics. Estimation of nonlinear models to stochastic phenomena is also elaborated.

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.

Application of the logistic, gompertz, and richards growth functions to gentan probability analysis

In a previous paper, a stochastic model complying with a state-dependent growth rate function was proposed for Gentan probability estimation. The growth function applied was the so-called Mitscherlich type of growth function. In this paper, application of other growth functions,i.e., the logistic, Gompertz and Richards growth functions, is addressed. Assuming growth dynamics as a function of time and state, an alternative stochastic model is derived with the above three growth dynamics. In the proposed model, the time is assumed to be continuous and the state to be discrete. Like in the previous paper, the sum of the Gentan probabilities derived from the proposed model with three growth functions over time is proved to be always unity. This is because the state-dependent part of the growth dynamics is a linear function of the state, which is the same as in the Mitscherlich growth function. This leads to the binomial probability law for a stochastic process, satisfying the unity requirement of the sum of the Gentan probabilities.

Japanese forest sector modeling through a partial equilibrium market model

The structure of Japanese timber markets has changed drastically during recent decades. After the introduction of a large amount of imported softwood products. Japanese timber producers have faced global competition with foreign timber suppliers such as Canada, the US, and recently Nordic countries. In this paper, we present a forest sector model for lumber markets with a focus on eight aggregate regions (Tohoku, Kanto, Hokuriku, Chubu, Kinki, Chugoku, Shikoku, and Kyushu) in Japan. The proposed model is based on the Samuelson-partial equilibrium formulation, which searches for an optimal solution by maximizing the net social payoff subject to demand and supply constraints. A nonlinear programming solution technique is incorporated into the proposed model. Three types of lumber are considered,i.e., domestic lumber, the lumber processed in Japan from imported logs, and imported lumber from the US and Canada. Using data for 1998, our analysis indicates that the derived equilibrium solution has a higher price for the imported lumber supply in all regions, and a lower price for the other two products in most regions than the actual current price in 1998. The derived net social payoff gains 1.6% compared with the one derived with the current set of prices and quantities.

Gentan probability analysis with a state-dependent discrete forest growth model

The previous stochastic models applied for Gentan probability estimation utilized either a stationary or nonstationary Poisson process to describe the forest owners’ harvesting behavior by means of the counting process. A nonstationary Poisson process has the advantage over a stationary Poisson process of capturing a time-dependent change of harvesting events. However, a nonstationary Poisson process can lack one preferred characteristic of the probability theory when utilizing an average growth function with an asymptotic nature of growth. That is, the sum of the derived Gentan probabilities over time does not always become unity. In this paper, we introduce a state-dependent discrete forest growth model with an asymptotic nature of growth to overcome the problem, then propose a stochastic model applied for Gentan probability estimation. The Mitscherlich type growth function is utilized. The derived probability law to capture the harvesting behavior is shown to be the binomial probability law. The derived probabilities prove to sum up to unity over time.