A BIOECONOMIC APPROACH TO THE FAUSTMANN–HARTMAN MODEL: ECOLOGICAL INTERACTIONS IN MANAGED FOREST

Abstract This paper develops a bioeconomic forestry model that makes it possible to take ecosystem services that are independent of the age structure of trees into account. We derive the Faustmann–Hartman optimal harvesting strategy as a special case. The bioeconomic model is then extended to account for the fact that forest harvesting decisions impact on other ecological resources, which provide benefits for the wider community. The paper focuses on impacts associated with disturbance caused by logging operations and habitat destruction due to tree removal. This enables us to explore the interactions between forest management and the dynamics of ecological resources. The optimal rotation rule is obtained as a variation on the traditional Faustmann–Hartman equation, where an additional term captures the potential benefits derived from the growth of the ecological resource valued at its shadow price. The steady‐state solutions to the problem and sensitivity to model parameter are identified using numerical analysis.     

21世纪海上丝绸之路沿线港口体系演化研究——基于Logistics、Lotka-Volterra模型

港口体系演化研究揭示21世纪海上丝绸之路沿线港口的发展规律,为我国相关企业海外港口投资提供决策支持,进而为我国“海上丝绸之路”战略的具体实施提供理论依据。本文利用生态种群演化相关理论,选取东南亚港口为数据样本来研究港口体系演化过程,研究发现港口规模演化趋势符合Logistics演化规律,2008年时增长速度达到峰值,2013年海上丝绸之路沿线港口体系进入衰退期,2030年左右港口体系规模将达到极限值;建立双种群增长的Lotka-Volterra模型和多种群增长模型研究新加坡港、巴生港、柔佛、槟城、丹戎帕拉帕斯的相互关系和演化趋势,提出我国在与这些港口合作时需要依据这种关系和演化趋势去统筹协调,才能达到效益最大化。     

Coordination between long-term decision process and day-ahead unit commitment in deregulated markets: A fuzzy hierarchical bi-level modeling approach

GenCos need the day-ahead unit commitment solutions in deregulated markets which are feasible, applicable in practice and consistent with the long-term planning decisions. However, such decisions are both vast in scope and different in nature so that applying a monolithic approach is subject to some difficulties and shortcomings. This paper aims to coordinate the long-term decision process with the day-ahead market scheduling through developing a profit-based fuzzy hierarchical bi-level approach. First, an annual planning model with monthly periods at power plant-generation technology level; then based upon a monthly scheduling with daily periods at generating unit level. An interactive solution method involving the soft coordination and feedback mechanisms using rolling horizon strategy is also presented. In the developed models, we try to address critical aspects of power system optimization. This approach is implemented for a real case and analytical results are reported.     

MANAGEMENT STRATEGY EVALUATION OF PHEROMONE‐BAITED TRAPPING TECHNIQUES TO IMPROVE MANAGEMENT OF INVASIVE SEA LAMPREY

We applied a management strategy evaluation (MSE) model to examine the potential cost‐effectiveness of using pheromone‐baited trapping along with conventional lampricide treatment to manage invasive sea lamprey. Four pheromone‐baited trapping strategies were modeled: (1) stream activation wherein pheromone was applied to existing traps to achieve 10^?12 mol/L in‐stream concentration, (2) stream activation plus two additional traps downstream with pheromone applied at 2.5 mg/hr (reverse‐intercept approach), (3) trap activation wherein pheromone was applied at 10 mg/hr to existing traps, and (4) trap activation and reverse‐intercept approach. Each new strategy was applied, with remaining funds applied to conventional lampricide control. Simulating deployment of these hybrid strategies on fourteen Lake Michigan streams resulted in increases of 17 and 11% (strategies 1 and 2) and decreases of 4 and 7% (strategies 3 and 4) of the lakewide mean abundance of adult sea lamprey relative to status quo. MSE revealed performance targets for trap efficacy to guide additional research because results indicate that combining lampricides and high efficacy trapping technologies can reduce sea lamprey abundance on average without increasing control costs.     

Un modelo predictivo de la evolución en costas rocosas

The recession of coastal cliffs is a widespread phenomenon on the rocky shores that are exposed to the combined incidence of marine and meteorological processes that occur in the shoreline. This phenomenon is revealed violently and occasionally as gravitational movements of the ground and can cause material or human losses. Their prediction is difficult; however it is basic for the proper coastal management and the clear understanding of erosion risks. There are several models of the coastal cliff recession processes. From the stochastic type models based on historical erosion events, to the theoretical models as described by Eikonal or Boussinesq equations. In this work an intermediate solution is adopted (process-response model), such as models based on simplified balance of forces as trigger mechanisms involved in the erosion of the rocks. This model fits the marine dynamics: sea level changes, tidal range and wave transformation; along with the evolution of the land: the slope of the surf zone, erosion and rock falls. So far these models have been limited to small slope cliffs, since its numerical stability and the propagation of errors are unknowns. For these reasons, the development of a generic model that reproduces the spatial and temporal evolution of a cliff-2D profile (platform, beach and slope) consisting on semi-consolidated heterogeneous materials, is presented. In addition, the computational implementation, the study of different numerical resolution techniques and the produced errors, are also exposed and analysed.     

A deterministic linear optimization model for allocating schools to zones

This paper presents a deterministic linear optimization model to support decisions on optimal allocation of schools to zones, its characterization and assignment of students, maximizing the social benefits of school owners and students. Students are assumed to show a multi-attribute behaviour, considering as important not only location, as is usual in the literature, but also quality of education and infrastructure, school costs and other attributes. There is heterogeneity of supply and demand. Students are classified by place of residence and socio-economic characteristics. Schools can be private, subsidized or free municipal ones. The model developed is applied to data of one of the municipalities of Santiago. The results obtained under different scenarios tend to confirm the expected demand's behaviour. This model could be used to guide decisions of both school owners or municipalities as well as students towards an equilibrium closer to a social optimum.     

Elliptic-Hyperbolic Systems and the Einstein Equations

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasi-linear elliptic-hyperbolic system of evolution equations. We prove that the Cauchy problem is locally strongly well posed and that a continuation principle holds.¶For initial data satisfying the Einstein constraint and gauge conditions, the solutions to the elliptic-hyperbolic system defined by the gauge fixed Einstein evolution equations are shown to give vacuum space-times.     

FROM HARVESTING TO NONHARVESTING UTILITY: AN OPTIMAL CONTROL APPROACH TO SPECIES CONSERVATION

The purpose of this paper is to retrace the evolution of mathematical models focused on relation and interaction between economic growth, sustainable development, and natural environment conservation. First, generic defensive expenditures are introduced into a common‐property harvesting model in order to favor the species growth. Second, a transition model comprising both harvesting and nonharvesting values of wildlife biological species emerges. The latter gives rise to a group of purely nonharvesting models where anthropic activities and economic growth may have positive or negative impact on the natural evolution of wildlife species. Several scholars have proved that optimal strategies that are relatively good for harvesting purposes are not simply “transferrable” to the context of conservation of wildlife biological species with no harvesting value. In addition, the existence of optimal policies for long‐term conservation of all biological species (with or without harvesting value) cannot be guaranteed without having relatively large species populations at the initial time. Therefore, all such strategies are incapable of enhancing the scarce populations of endangered species and, therefore, cannot save these species from eventual (local) extinction. As an alternative, policymakers may soon be compelled to design and implement short‐term defensive actions aimed at recovery and enhancement of endangered wildlife species.     

货架展示量与定价模型及供应链协调分析

针对单生产商和单零售商组成的供应链,假定需求依赖于货架展示量与零售价格,分别建立了集中式控制下和分散式控制下的货架展示量与定价决策模型,给出了协调供应链的批发价加货架补贴合同。针对单生产商和n个零售商组成的供应链,假定总需求是n个零售商的总货架展示量和平均零售价格的函数、每个零售商的需求与其货架展示相关的促销努力成正比,分析了相应的集中式与分散式决策,并给出了协调供应链的批发价加货架补贴加转移支付合同。     

The hyperbolic mean curvature flow

We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector. The flow stems from a geometrically natural action containing kinetic and internal energy terms. As the mean curvature of the hypersurface is the main driving factor, we refer to this model as the hyperbolic mean curvature flow (HMCF). The case that the initial velocity field is normal to the hypersurface is of particular interest: this property is preserved during the evolution and gives rise to a comparatively simpler evolution equation. We also consider the case where the manifold can be viewed as a graph over a fixed manifold. Our main results are as follows. First, we derive several balance laws satisfied by the hypersurface during the evolution. Second, we establish that the initial-value problem is locally well-posed in Sobolev spaces; this is achieved by exhibiting a convexity property satisfied by the energy density which is naturally associated with the flow. Third, we provide some criteria ensuring that the flow will blow-up in finite time. Fourth, in the case of graphs, we introduce a concept of weak solutions suitably restricted by an entropy inequality, and we prove that a classical solution is unique in the larger class of entropy solutions. In the special case of one-dimensional graphs, a global-in-time existence result is established.     

The hyperbolic mean curvature flow

We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector. The flow stems from a geometrically natural action containing kinetic and internal energy terms. As the mean curvature of the hypersurface is the main driving factor, we refer to this model as the hyperbolic mean curvature flow (HMCF). The case that the initial velocity field is normal to the hypersurface is of particular interest: this property is preserved during the evolution and gives rise to a comparatively simpler evolution equation. We also consider the case where the manifold can be viewed as a graph over a fixed manifold. Our main results are as follows. First, we derive several balance laws satisfied by the hypersurface during the evolution. Second, we establish that the initial-value problem is locally well-posed in Sobolev spaces; this is achieved by exhibiting a convexity property satisfied by the energy density which is naturally associated with the flow. Third, we provide some criteria ensuring that the flow will blow-up in finite time. Fourth, in the case of graphs, we introduce a concept of weak solutions suitably restricted by an entropy inequality, and we prove that a classical solution is unique in the larger class of entropy solutions. In the special case of one-dimensional graphs, a global-in-time existence result is established.     

Relaxation schemes for curvature‐dependent front propagation

In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature‐dependent local law. In the Chapman‐Enskog expansion, this relaxation approximation leads to the level‐set equation for transport‐dominated front propagation, which includes the mean curvature as the next‐order term. This approach yields a new and possibly attractive way of calculating numerically the propagation of curvature‐dependent fronts. Since the relaxation system is a symmetrizable, semilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature‐dependent front propagation without discretizing directly the complicated yet singular mean curvature term. © 1999 John Wiley & Sons, Inc.     

Coordinating ordering and pricing decisions in a two-stage distribution system with price-sensitive demand through short-term discounting

We consider a short-term discounting model in which the distributor offers a discounted price for the retailers’ orders placed at the beginning of its replenishment cycle, in a non-cooperative distribution system with one distributor and multiple retailers, each facing price-sensitive demand. We examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers’ ordering and pricing decisions under two common types of demand, linear demand in price and constant elasticity demand in price. Our numerical study reveals that, in the presence of homogeneous retailers (namely, retailers with identical demand rates), the distributor’s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases, but increases as price elasticity increases. Although an increase in the inventory holding cost rate has a negative effect on the distributor’s profit, it may have a positive effect on the retailers’ profits. We further find that with heterogeneous retailers (namely, retailers with different demand rates), offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large. This cross effect, however, is absent under constant elasticity demand.     

DO ACCURATE STOCK ESTIMATES INCREASE HARVEST AND REDUCE VARIABILITY IN FISHERIES YIELDS?

Abstract Fisheries managers normally make decisions based on stock abundance estimates subject to process, observation, and model uncertainties. Considerable effort is invested in gathering information about stock size to decrease these uncertainties. However, few studies have evaluated benefits from collecting such information in terms of yield and stability of annual harvest. Here, we develop a strategic age‐structured population model for a long‐lived fish with stochastic recruitment, resembling the Norwegian spring‐spawning herring (NSSH, Clupea harengus L.). We evaluate how uncertainties in population estimates influence annual yield, spawning stock biomass (SSB), and variation in annual harvest, using both the proportional threshold harvesting (PTH) and the current harvest control rule for NSSH as harvest strategies. Results show that the consequences of a biased estimate are sensitive to the harvest strategy employed. If the harvest strategy is suitably chosen, the benefits of accurate information are low, and less information about the stock is necessary to maintain high average yield. Reduced harvest intensity effectively removes the need for accurate stock estimates. PTH (a variant of the constant escapement strategy) with low harvest ratio and the current NSSH harvest control rule both provide remarkable stability in yield and SSB. However, decreased uncertainty will often decrease year‐to‐year variation in harvest and the frequency of fishing moratoria.     

Single versus multiple supplier sourcing strategies

Successful supply chain management necessitates an effective sourcing strategy to combat uncertainties in both supply and demand. In particular, supply disruption results in excessive downtime of production resources, upstream and downstream supply chain repercussions, and eventually a loss in the market value of the firm. In this paper we analyze single period, single product sourcing decisions under demand uncertainty. Our approach integrates product prices, supplier costs, supplier capacities, historical supplier reliabilities and firm specific inventory costs. A unique feature of our approach is the integration of a firm specific supplier diversification function. We also extend our analysis to examine the impact of minimum supplier order quantities. Our results indicate that single sourcing is a dominant strategy only when supplier capacities are large relative to the product demand and when the firm does not obtain diversification benefits. In other cases, we find that multiple sourcing is an optimal sourcing strategy. We also characterize a non-intuitive trade-off between supplier minimum order quantities, costs, and supplier reliabilities. Finally, we examine the robustness of our results through an extensive numerical analysis of the key parameters of our model.     

Ermakov–Ray–Reid Systems in (2+1)‐Dimensional Rotating Shallow Water Theory

A (2+1)‐dimensional rotating shallow water system with an underlying circular paraboloidal bottom topography is shown to admit a multiparameter integrable nonlinear subsystem of Ermakov–Ray–Reid type. The latter system, which describes the time evolution of the semi‐axes of the elliptical moving shoreline on the paraboidal basin, is also Hamiltonian. The complete solution of the generic eight‐dimensional dynamical system governing the reduction is obtained in terms of an elliptic integral representation.     

The first eigenvalue of Laplace operator under powers of mean curvature flow

In this paper, we derive the evolution equation for the first eigenvalue of Laplace operator along powers of mean curvature flow. Considering a compact, strictly convex n-dimensional surface M without boundary, which is smoothly immersed in R n+1 , we prove that if the initial 2-dimensional surface M is totally umbilical, then the first eigenvalue is nondecreasing along the unnormalized H k -flow. Moreover, as applications of the evolution equation, we construct some monotonic quantities along this kind of flow.     

三维洛仑兹空间形式中的类光曲线

讨论三维洛仑兹空间形式中的类光曲线粒子模型,研究依赖于粒子轨道的Cartan曲率的作用,找出了沿着极值曲线的Killing场,通过Killing场构造合适的坐标系,用积分求出极值曲线的参数表达式.     

L 2 Forms and Ricci Flow with Bounded Curvature on Complete Non-Compact Manifolds

In this paper, we study the evolution of L ² one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the L ² norm of a smooth one form is non-increasing along the Ricci flow with bounded curvature. The L ^∞ norm is showed to have monotonicity property too. Then we use L ^∞ cohomology of one forms with compact support to study the singularity model for the Ricci flow on .     

A deterministic‐control‐based approach motion by curvature

The level‐set formulation of motion by mean curvature is a degenerate parabolic equation. We show that its solution can be interpreted as the value function of a deterministic two‐person game. More precisely, we give a family of discrete‐time, two‐person games whose value functions converge in the continuous‐time limit to the solution of the motion‐by‐curvature PDE. For a convex domain, the boundary's “first arrival time” solves a degenerate elliptic equation; this corresponds, in our game‐theoretic setting, to a minimum‐exit‐time problem. For a nonconvex domain the two‐person game still makes sense; we draw a connection between its minimum exit time and the evolution of curves with velocity equal to the “positive part of the curvature.” These results are unexpected, because the value function of a deterministic control problem is normally the solution of a first‐order Hamilton‐Jacobi equation. Our situation is different because the usual first‐order calculation is singular. © 2005 Wiley Periodicals, Inc.