Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

TEMPORAL AGGREGATION AND TESTING FOR TIMBER PRICE BEHAVIOR

ABSTRACT. Different harvest timing models make different assumptions about timber price behavior. Those seeking to optimize harvest timing are thus first faced with a decision regarding which assumption of price behavior is appropriate for their market, particularly regarding the presence of a unit root in the timber price time series. Unfortunately for landowners and investors, the literature provides conflicting guidance on this subject. One source for the ambiguous results of unit root tests of timber prices may involve data problems. We used Monte Carlo simulations to show that aggregating observations below their observed rate resulted in similar power reductions and empirical size distortions across three classes of unit root tests. Moving‐average error structures can also affect power and sizes of tests on period‐averaged data. Such error structures can also be created by the kind of temporal averaging common in reported timber prices. If we take timber prices at their face value and therefore ignore these sampling error and temporal aggregation complications, we find that unit root tests on southern timber prices support a unit root in 158 out of 208 product‐deflation combinations tested, random walks in 38 of the series found to be nonsta‐tionary, and stationarity in none. However, if we recognize temporal aggregation errors, unit root tests more commonly favor stationarity, especially for pulpwood stumpage. Because price trends for sawtimber and pulpwood products may behave differently even in the same region, stochastic harvest timing models must be developed that allow their multiple products to follow different price paths.     

TIMBER SUPPLY UNDER DEMAND UNCERTAINTY: WELFARE GAINS FROM PERFECT COMPETITION WITH RATIONAL EXPECTATIONS

ABSTRACT. This paper presents a noneconometric approach to estimating the short‐run timber supply function based on optimal harvest decisions. Determination of optimal harvest levels and estimation of supply function coefficients are integrated into one step by incorporating a parametric short‐run timber supply function into the harvest decision model. In this manner we convert the original harvest decision model into a new optimization problem with the supply function coefficients functioning as “decision variables.” Optimal solution to the new decision model gives the coefficients of the short‐run supply function and, indirectly, the optimal harvest levels. This approach enables us to develop stochastic models of the timber market that are particularly useful for forest sector analysis involving comparison of alternative institutional regimes or policy proposals and when the timber market is affected by stochastic variables. For demonstration purposes, we apply this method to compare the performances of two timber market regimes (perfect competition and monopoly) under demand uncertainty, using the Swedish data. The results show that the expected timber price is 22 percent lower and the expected annual timber supply is 43 percent higher in the competitive market than in the monopoly market. This confirms the theoretical result that monopoly reduces supply and increases price. The expected social welfare gain from perfect competition over monopoly is about 24 percent.     

Timber harvest scheduling with price uncertainty using Markowitz portfolio optimization

Harvest scheduling models need to account for uncertain revenue predictions when minimizing risk of financial loss is an important management objective. In this paper, we present methods for estimating the means and covariances of stumpage prices and incorporating them in harvest scheduling models. We approached the estimation problem by fitting time-series models to loblolly pine sawtimber and pulpwood stumpage prices in Georgia, USA, and deriving formulas for means and covariances of price predictions. Statistical evidence supported integrated autoregressive models, which caused covariances of price predictions to increase with time. The means and covariances of price predictions were combined with timber yield and land value predictions to give exact formulas for the revenue means and covariances of timber management activities. Sawtimber regimes dominated pulpwood regimes by providing higher mean revenues across a wide range of revenue variances. Harvest scheduling results for a hypothetical forest of pine plantations showed that the forest plan that maximized mean income without concern for risk (expressed as the standard deviation of income) involved sawtimber production with a 35-year rotation age. Risk was reduced 30% with little effect on mean income by using shorter-rotation sawtimber regimes. Risk was reduced 80% by using a mix of short-rotation sawtimber and pulpwood regimes because pulpwood price was only weakly correlated with sawtimber price. The latter risk-reduction came at the expense of mean income, which was reduced by as much as 50%. The risks and compositions of optimal forest plans were extremely sensitive to assumptions about the range of future prices that were inherent in different prediction models. This sensitivity emphasizes the importance of carefully determining the decision makers beliefs about stumpage price behavior.     

Structured products equilibria in conic two price markets

A novel equilibrium theory is developed for two price markets permitting investors to trade personally designed structured products. Classical market clearing is enhanced for structured products where the market allows these products to be freely bought at ask prices or sold for bid prices. Competitive pressures lead the market to lower the ask prices and raise the bid prices with the market offering individual investors the widest possible set of acceptable risks provided the aggregate counter cash flow held by the market is consistent with a more conservative prespecified set of acceptable risks. We learn that in equilibrium heterogeneous investors inherit a common hedging objective of maximizing the bid prices of the final structured product sold to market or equivalently minimizing the ask price of what is bought.     

OPTIMAL TIMING OF SALVAGE HARVEST IN RESPONSE TO A STOCHASTIC INFESTATION

Abstract Following a catastrophic disturbance, forest managers may choose to perform a salvage harvest to recoup timber losses. When the disturbance process evolves stochastically, a unique option value arises associated with the salvage harvest decision. This option value represents the value of postponing a salvage harvest to gain more information about the disturbance process. This paper uses a real options approach to determine how much of a forested area must be infested to trigger a salvage harvest when the forest provides both timber and nontimber values. Analytical results indicate slower rates of forest recovery will optimally delay a salvage harvest while forested areas with large timber values and where nontimber values are more sensitive to the presence of dead and dying trees should be harvested more immediately. The model is applied to a mountain pine beetle outbreak in Idaho's Sawtooth National Forest using readily available aerial detection survey data.     

A point‐input,point‐output forest as a microprototype for capital accounting

The point‐input, point‐output, plantation forest was first studied by Martin Faustmann in the mid‐19th century. The exploitation of a Faustmannian forest involves decisions concerning investments and receipts over time that are qualitatively different from the smooth, convex flows that are usually studied in the economics of accounting. The simple, well understood analysis of the forest has implications for the concept of income in forestry as well as in other industries that are typified by nonconvex decisions. A forest is a salient example of the importance of discrete, irreversible investment, and of the role of price effects (capital gains) in income accounting and, more fundamentally, of perceptions of the “right prices” in economic analysis.     

电力市场中合同电量与竞争电量交易比例的研究

在单边开放的区域电力市场中,合理的合同电量与竞争电量交易比例是保证电力市场有效运行的一个重要环节。竞争电量所占的比例将主要取决于当前发电公司的市场行为。首先使用BP神经网络对电力需求弹性系数进行了预测,然后以长期电力市场均衡为目标函数,考虑贵州电网发电机组的可用容量与负荷预测的误差,以及贵州输电线路的可靠性诸因素,推导出合同电量与竞争电量交易比例,经过与南方区域电力市场目前运营规则规定的交易比例比较,该比例是合理的,可以规避电力市场价格波动等带来的风险。     

A system for the design of short term harvesting strategy

Short term harvesting requires decisions on which stands to harvest, what timber volume to cut, what bucking patterns (how to cut up the logs) to apply to logs in order to obtain products that satisfy demand and which harvesting machinery to use. This is an important problem in forest management and difficult to solve well in satisfying demand, while maximizing net profits. Traditionally, foresters have used manual approaches to find adequate solutions, which has shortcomings both in time spent by analysts and the quality of solutions. Since demand for timber products is defined by length, diameter and quality of each piece, this leads to a complex combinatorial problem in matching supply (standing trees) and demand. We developed one of the few reported approaches for solving the short term harvesting problem based on a computerized system, using a linear programming approach. Determining adequate bucking patterns is not trivial. We develop a column generation approach to generate such patterns. The subproblem is a specially designed branch and bound scheme. The generation of bucking patterns implemented within the LP formulation led to a significant improvement of solutions. We believe this is the first system implemented with this level of detail. This system has been advantageously implemented in several forest companies. The results obtained show improvements obtained by the firms of 5–8% in net revenues over traditional manual approaches.     

Forestry management under uncertainty

The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage Stochastic Integer Programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.     

Design of insurance contracts using stochastic programming in forestry planning

This work addresses a tactical planning problem faced by a forestry firm, deciding which timber units to harvest and what roads to build to obtain the greatest possible benefits. We include uncertainty in prices by means of utility theory. This enables solutions to be found that the firm finds preferable to those obtained when risk aversion is ignored and makes it possible to design insurance contracts that benefit the firm while also being attractive to an insurer. Two types of contract are designed; one dependent on the firm’s operating result and the other independent of it. Metrics are then developed to quantify the benefits conferred by a contract, demonstrating that the latter contract type dominates the former. These results are then illustrated by applying them to a simplified planning problem of a forest owned by the Chilean forestry operator Millalemu.     

Green product development under competition: A study of the fashion apparel industry

Motivated by the observed industrial issues, we analytically develop a fashion supply chain consisting of one manufacturer and two competing retailers and investigate how retail competition and consumer returns affect green product development in fashion apparel. In the basic model, that is, the pure “product greenness level” game, we find that the optimal greenness level of the fashion product decreases along with the level of market competition. This finding implies that a more competitive market leads to a lower optimal greenness level. We also identify that when the consumer return rate increases, the optimal product greenness level is substantially reduced. In the extended model with joint decisions on greenness and pricing, we find that the optimal product greenness level for the whole channel is always higher in the scenario when both retailers charge a higher retail price than in the case with a lower retail price. As such, the underdevelopment of green fashion products is a result of fashion industry features, such as an extremely competitive environment for green product development, relatively low retail prices for fashion products, and high consumer return rates. Therefore, fashion companies should join a co-opetition game for the green product market and simultaneously enhance their efficiency in managing consumer returns. To support our analytical findings, we conduct extensive industrial interviews with various representative companies. Based on this multi-methodological approach (MMA), this paper generates practice-relevant managerial insights that not only contribute to the literature, but also act as valuable references for industrialists.     

Risk-averse order policies with random prices in complete market and retailers’ private information

We consider a retailer who orders products before the price for them becomes known. The price is an outcome of perfect competition in a complete market. Since the demand is price sensitive, the uncertainty in prices induces uncertain profits and associated risks. In this paper we show that if the retailer is risk averse and, as a result, selects a utility function of profit to maximize, then his subjective assessment of future prices is affected by the risk attitude. This, in turn, introduces a bias in retailer’s ordering policies. By considering coordinated pricing and ordering policies we derive a relationship between risk aversion, retailer’s subjective (private) assessment and the market implied, risk neutral forecast. This relationship and the induced bias are then illustrated for two typical operations management strategies which involve either inventory considerations or promotions avoiding accumulation of stocks.     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

考虑海外代购的品牌商定价模型研究

随着海外代购体量的日趋增大,代购带来的低价威胁对于在不同国家不同市场销售产品的公司来说已经成为一个日益严重的问题。同时,代购渠道中假货的问题也愈发严重。因此,在海外代购背景下探究产品定价模型具有必要性。以往研究普遍认为这种未经授权的销售会削减品牌方的利润,但实则不然。基于这一发现,本研究为在两个不同市场销售相同产品但面临代购低价威胁的公司制定考虑代购的市场定价模型。由公司制定两个市场的价格,消费者选择是否从包括代购在内的三个渠道购买产品。推出两个授权市场的最优价格,分析各参数变化对最优价格的影响,并校验最优价格对消费者需求和总利润的影响。模型分析表明,高价市场中有部分消费者需求转向海外代购,同时低价市场的消费者需求也受到了影响,且在一定条件下,提高高价市场的产品定价能够扩大低价市场的需求,从代购的角度解释了现实中需求曲线向上倾斜的现象。此外,两个独立市场之间的价格差距对代购市场的销售也产生了积极影响,并且在某些条件下,增大价格差距可以提高公司的收益水平。随后讨论了一种极端模型和三种扩展模型,通过模型分析表示,扩展后的定价模型也显示出与基础市场模型相似的灵敏度分析结果,同样得到两个市场的价差扩大会导致代购市场的销售额增加的结论,并且在一定条件下,公司的利润更高,增加了结论的可信度。     

Average shadow price and equilibrium price: A case study of tradable pollution permit markets

Shadow prices indicate implicit values of limited resources at the margin and provide important information in decision making for resource management. In continuous economic models, shadow prices associated with demand-supply balance constraints represent consumers’ willingness to pay and producers’ marginal cost, hence they correspond to market equilibrium prices. As well known, however, marginal analysis fails in the case of discrete optimization, such as mixed integer programming. An alternative concept has been introduced in the literature to measure the value of an extra unit of a limited resource in such cases. This concept is based on average rather than marginal values, thus called the average shadow price, and interpreted in the same way as conventional shadow prices. Whether average shadow prices in a discrete economic model can serve as market equilibrium prices has not been addressed in the related literature. The present paper addresses this issue in an empirical setting. Using a tradable pollution permit market as an example, where firms’ YES/NO type technology adoption decisions are represented by binary variables, we show that the average shadow price of tradable permits can be interpreted as the equilibrium price only when certain conditions related to the cost structure and emission levels hold. On the other hand, we show that an iterative procedure based on individual firms’ cost minimizing behavior presents a better approach for finding a price that can eliminate or reduce the gap between demand and supply of permits in the market.     

双渠道销售差别定价闭环供应链协调应对生产成本扰动研究

针对一个新产品和再造品存在差别定价,且两类产品通过不同销售渠道进行销售的闭环供应链,构建了一个基本的两部收费契约协调模型。随后,考虑突发事件同时干扰新产品和再造品生产成本的情况下,集中式决策闭环供应链的最优决策问题,并设计了可协调成本扰动下双渠道销售差别定价闭环供应链的两部收费契约。研究表明:在集中式决策闭环供应链中,相比于稳定环境下新产品和再造品的最优决策,生产成本扰动下两类产品最优产量的调整方式不仅与生产成本扰动的程度相关,还与两类产品之间的相互替代系数相关,且改进的两部收费契约以系统各成员共担风险的方式实现了闭环供应链协调的目的。     

Modeling short‐term post‐offering price–volume relationships using Bayesian change‐point panel quantile regression

We propose a special panel quantile regression model with multiple stochastic change‐points to analyze latent structural breaks in the short‐term post‐offering price–volume relationships in China's growth enterprise market where the piecewise quantile equations are defined by change point indication functions. We also develop a new Bayesian inference and Markov chain Monte Carlo simulation approach to estimate the parameters, including the locations of change points, and put forth simulation‐based posterior Bayesian factor tests to find the best number of change points. Our empirical evidence suggests that the single change point effect is significant on quantile‐based price–volume relationships in China's growth enterprise market. The lagged initial public offering (IPO) return and the IPO volume rate of change have positive impacts on the current IPO return before and after the change point. Along with investors' gradually declining hot sentiment toward a new IPO, the market index volume rate of change induces the abnormal short‐term post‐offering IPO return to move back to the equilibrium. Copyright © 2015 John Wiley & Sons, Ltd.     

期权合约在订单农业中的应用

订单农业作为一种基于远期合约的农产品销售模式,被认为是解决农产品流通困难问题并实现农业产业化经营的重要出路,但订单农业的价值由于其普遍存在的违约现象而大打折扣。本文在合约不完全性的前提下,用一个简单的单期保护价模型说明了生产条件和市场条件的不可预知性是订单农业违约的根本原因,并证明此时一定存在农产品专用性投资不足的问题。而低水平的专用性投资既降低了履约的概率,又降低了订单交易所能产生的附加值。在此基础上,本文给出了一种具有期权性质的农产品合约,并证明经过相应的再谈判程序,期权合约既可以像传统订单合约一样帮助农户规避市场风险,又可以解决传统订单下无效率的单方面毁约问题。最后,本文证明了在期权合约下,农户和农产品收购商都将作出最优水平的专用性投资,低水平专用性投资带来的低附加值问题由此得到解决。     

期权视角下房屋预售合约定价模型

房屋预售合约赋予了购房者以给定的价格购买房屋的权利,具有期权性质。首先基于房地产市场具有摩擦的事实,将房屋预售合约视为房价的期权合约,然后通过将房价演变过程模型化为Ornstein-Uhlenbeck过程,导出了预售合约的合理价格(即首付)的解析表达式,最后比较了采用几何布朗运动与Ornstein-Uhlenbeck过程模拟房价变化所得房屋预售价格的差异。结论认为,基于Ornstein-Uhlenbeck过程导出的房屋预售合约价格相较于几何布朗运动下的预售合约价格具有更小的套利空间。