A MIXED CONTROL PROBLEM OF THE MANAGEMENT OF NATURAL RESOURCES

In this paper, we study the optimal solutions of a model of natural resource management which allows for both impulse and continuous harvesting policies. This type of model is known in the literature as mixed optimal control problem. In the resource management context, each type of control represents a different harvesting technology, which has a different cost. In particular, we want to know when the following conjecture made by Clark is an optimal solution to this mixed optimal control problem: if the harvesting capacity is unlimited, it is optimal to jump immediately to the steady state of the continuous time problem and then to stay there. We show that under a particular relationship between the continuous and the impulse profit function, the conjecture made by Clark is true. In other cases, however, it is either better to use only continuous control variables or to jump to resource levels which are smaller than the steady state and then let the resource grow back to the steady state. These results emphasize the importance of the cost functions in the modeling of natural resource management.     

人力资源成本预算与控制的理论分析

本的分析是人力资源成本管理体系研究的一部分，着重于探讨在人力资源成本管理体系中，人力资源成本的预算与控制与该体系中其他几部分之间的关系，研究人力资源成本管理实践中成本预算与控制的理论基础，并提出一些新的思路。     

带凸资源和恶化效应的单机松弛窗口排序

研究带凸资源和恶化效应的单机窗口指派排序问题,其中窗口指的是松弛窗口,凸资源和恶化效应指的是工件的实际加工时间是其开始加工时间的线性函数,是其资源消耗量的凸函数。目标是确定工件的加工顺序,资源分配量以及窗口的开始加工时间和长度使其在总资源消耗费用(与窗口有关的排序费用)有上界限制的条件下,极小化与窗口有关的排序费用(总资源消耗费用)。获得了求解上述问题的最优算法,证明了该问题是多项式时间可解的。     

FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

In this study, we consider scheduling problems with convex resource dependent processing times and deteriorating jobs, in which the processing time of a job is a function of its starting time and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately. This paper focus on the single-machine problems with objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. It shows that the problems remain polynomially solvable under the proposed model.     

具有凸资源约束的单机指数学习效应问题

研究在所有工件的正常加工时间均相同的情况下具有指数学习效应和凸资源约束的单机排序问题.给出了两种模型:在资源消耗总费用有限的情况下,以工件的最大完工时间为目标函数;在工件的最大完工时间有限的情况下,以资源消耗总费用为目标函数.求两种模型下的最优排序和最优资源分配,使得目标函数最小.证明这两个问题都是多项式时间可解的,并给出了相应的算法.     

An empirical re-examination of natural resource scarcity and economic growth

This paper is concerned with the effect of natural resource scarcity on economic growth in the United States. After defining the notion of scarcity and introducing two measures of scarcity—unit costs and relative resource price—changes in resource scarcity trends for lead, zinc, nickel, aluminium, silver, iron and copper over the most recent three decades are investigated. Only for silver and iron is there any indication that such a change has occurred. For silver, the change is transitory. To the extent that change takes place, it has implications for future economic growth, i.e. natural resource scarcity and economic growth are interrelated. To see whether this is a relevant concern, subsequent to the examination of changing resource scarcity trends an objective effort is made to identify a long-run equilibrium relationship between natural resource scarcity and economic growth. Relying on cointegration techniques, only for the unit cost measure for lead and copper for one of the measures of cointegration is there a suggestion that natural resource scarcity has affected economic growth in the United States over the period 1889–1992.     

Unrelated parallel-machine scheduling with position-dependent deteriorating jobs and resource-dependent processing time

This paper is to analyze unrelated parallel-machine scheduling resource allocation problems with position-dependent deteriorating jobs. Two general resource consumption functions, the linear and convex resource, are investigated. The objectives are to minimize the cost function that includes the weights of total load, total completion time, total absolute deviation of completion time, and total resource cost. Moreover, we try to minimize the cost function that includes the weights of total load, total waiting time, total absolute deviation of waiting time, and total resource cost. Although each job processing time can be compressed through incurring an additional cost, we show that the problems are polynomial time solvable when the number of machines is fixed.     

Cost thresholds for dynamic resource location

The traditional dynamic resource location problem attempts to minimize the cost of servicing a number of sequential requests, given foreknowledge of a limited number of requests. One artificial constraint of this problem is the presumption that resource relocation and remote servicing of requests have identical costs. Parameterizing the ratio of relocation cost to service cost leads to two extreme behaviors in terms of dynamic optimizability. The threshold at which a specific graph transitions between these behaviors reveals certain characteristics of the graph's decomposability into cycles.     

人力资源约束下的项目群调度问题建模与求解

基于人员胜任力是影响工作绩效的关键因素,将资源受限项目调度问题中的可更新资源通过一系列科学合理的方法或者手段转变为存在胜任力差异的人力资源,由此构建起一个强调胜任力差异的人力资源约束项目调度问题模型,此模型最突出的优势在于选取了能够客观合理评估人员胜任力的指标,提供了严谨科学的关系式,将复杂的多项目总工期与总成本的双目标最小化问题转换为综合指标单目标最大化问题,建立数学优化模型,采用遗传算法求解。通过算例研究证实,相较于传统多模式模型,基于人员胜任力水平差异的模型明显更胜一筹,其优势集中表现为最优工期更短、最优成本更低。考虑了胜任力差异的数学优化模型更符合研发项目群管理实践,同时遗传算法在求解方面不仅效率高,并且更容易获得客观准确的结果。     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.     

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.     

NONRENEWABLE RESOURCE EXTRACTIONS WITH A POLLUTION SIDE EFFECT: A COMPARATIVE DYNAMIC ANALYSIS

ABSTRACT. In this paper, we present a nonrenewable resource model including environmental pollution as a state variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The costate variable for the resource stock is decomposed into a scarcity effect and a cost effect; and the costate variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.     

基于收益管理和仿真的第三方仓储资源分配

针对不确定市场需求条件下第三方仓储资源的能力规划与分配问题,构建随机数学规划模型,理论分析证明了最优资源分配量的存在性,并指出最优资源分配量是单位资源成本的递减函数、单位资源收益和单位损失成本的递增函数。鉴于解析求解的复杂性,基于收益管理思想,结合离散事件仿真技术和响应曲面法,提出一种新的分析求解框架:收益管理用于细分顾客、构建资源分配策略,仿真模型刻画系统随机特性并评估系统绩效指标,响应曲面法则优化分配策略并探寻绩效改进方向。案例研究和仿真实验结果显示,根据顾客类别分配仓储能力的策略优于传统的先到先服务策略,收益管理、响应曲面法与仿真的综合集成,能够提高系统收益,从而使本文所提方法体系得到了有效验证。     

Resource allocation on condition of random resource demand of network activities

A general network model is considered. Each activity may require several storable and productive resources. Fixed amounts of storable resources are delivered at fixed times. The capacities of the productive resources are assumed to be constant. A general resource allocation problem is derived in order to optimize the cost for the execution of the network activities, In the main, the case is considered where the resource demands of the activities are random variables. For this case, the means of resource demands are estimated and a method is presented to obtain a vector of start times and durations of the activities so that a cost function is minimized and the probability that, at any time, there appears no lack of resources is maximized.     

油价波动和资源环境补偿视角下石油资源税率研究——基于山东省数据

油价、资源与环境统筹管理政策缺失导致石油资源外部性问题日益严重,从油价波动和资源环境补偿视角出发研究石油资源税率是解决石油资源外部性,实现对油价、资源与环境统筹管理的关键。基于山东省2000~2013年石油资源开采行业数据,根据使用者成本法测算山东省石油开采行业的资源耗减成本,发现当前资源税费比率应提高14%;根据生态补偿标准模型测算生态环境成本,结合大量实地调研,指出生态环境补偿水平应从目前补偿水平的22%逐步提高至完全补偿生态环境成本。然后,根据价值对等原则构建资源生态环境补偿方程,探索性地计算了基于油价波动的石油资源税率,发现当油价处于(23~52)、(52~78)、(78~115)美元/桶的油价区间时,在7%折现率下分别对应17.51%、18.84%、19.04%的补偿税率,得出结论:当前条件下将资源税费与环境补偿费用合并征收,需要将补偿税率逐步提高至15%~20%。最后,从税率确定、计征方式以及监管体系三方面提出了执行对策。     

不确定条件下环境友好型资源分配二层规划模型

本文讨论了不确定条件下环境友好型的资源分配问题:其中总公司作为上层领导者在各下属工厂间合理分配资源,以期获得最大收益的同时降低对环境的污染程度;而作为下层从属者的各工厂决定各自产量以期获得最大利润。该问题中的产品价格、生产成本、资源成本等被考虑为随机变量,环境污染指数被考虑为模糊变量,因而本文构造了不确定条件下的机会约束二层资源分配模型。运用等价定理对模型进行转换,并采用交互式满意度法将二层模型转化为单层模型以便求解。最后通过数值算例证实了模型和算法的可行性与有效性。此外,由于模型含有影响模型解的参数,故基于满意度和置信水平分别进行了灵敏度分析,进一步验证了所提出模型的科学性。     

Equilibrium path in oligopolistic market of nonrenewable resource

In this paper we study the oligopoly model of nonrenewable resource in which the unit production cost is variable and depends on the resource reserve level. We consider both the open-loop strategy and the closed-loop strategy of this dynamical differential game. For the case of linear cost function we have observed that the open-loop equilibrium and the self-feedback equilibrium satisfy the same equilibrium conditions, which can be described as a dynamical system. The analysis shows that the equilibrium path of the model is the stable orbit of this system, and this result leads to further studies of the properties of the total extraction and reserve and the individual ones of each producer. For the total extraction rate and reserve, some of the properties are similar to those of most oligopoly models with fixed unit production cost. For the individual behaviors, we have found out the solution expressions of the individual extraction rate and resource reserve and got the main result that the producer with larger initial stock has a larger but declining market share and the share of each producer converges toward the average one when time approaches to infinite.     

A note on the paper ‘On dynamical multi-team Cournot game in exploitation of a renewable resource’

In a recent paper (Asker, 2007) [1] a dynamic Cournot oligopoly game is proposed and it is claimed that this model represents competition among firms that exploit a common access natural resource. According to the author’s claim, the feature that relates the model with renewable natural resource harvesting is given by the presence of a particular cost function where the total cost of each fisherman is proportional to the square of the own quantity of harvesting and inversely proportional to the total harvesting quantity. In contrast, the usual function used in the literature on the exploitation of natural resources (such as fisheries) is inversely proportional to the available resource stock, and not to the total harvesting. This, in some sense, assumes exactly the opposite (as the available resource is inversely proportional to the total harvesting). So, we believe that the paper (Asker, 2007) [1] contains an error which is probably due to a misunderstanding or a misreading and misinterpretation of the (well-established) literature on bioeconomic modelling, but nevertheless misleading to researchers interested in bioeconomic modelling. The aim of this short note is to explain the mistake and to summarize the correct derivation and interpretation of the cost function. Our goal is to avoid the propagation of a subtle (but nevertheless misleading) error.     

基于需求的实时网络定价策略

价格作为一种网络拥塞控制管理与资源分配的机制不断地表现出较高的效率。基于对网络使用实际流量的信息，本提出了一种实时的网络定价策略——基于需求的实时网络定价策略。该定价策略由三部分构成：固定连接费、资源使用费及网络拥塞费。与传统的定价策略相比，基于需求的实时网络定价策略更能反映实际的需求情况，在网络拥塞控制管理与网络资源分配等方面有更高的效率。