A heuristic approach to stochastic cutoff grade optimization for open pit mining complexes with multiple processing streams

Cutoff grade specifies the available supply of metallic ore from an open pit mine to the multiple processing streams of an open pit mining complex. An optimal cutoff grade strategy maximizes the net present value (NPV) of an open pit mining operation subject to the mining, processing, and marketing/refining capacity constraints. Even though, the quantities of material flowing from the mine to the market are influenced by the expected variation in the available metal content or inherent uncertainty in the supply of ore, the majority of cutoff grade optimization models not only disregard this aspect and may lead to unrealistic cash flows, but also they are limited in application to an open pit mining operation with single processing facility. The model proposed herein determines the optimal cutoff grade policy based on a stochastic framework that accounts for uncertainty in supply of ore to the multiple ore processing streams. An application on a large-scale open pit mining operation develops a unique cutoff grade policy along with a portfolio of mining, processing, and marketing/refining rates. Owing to the geological uncertainty, the approach addresses risk by showing a difference of 14% between the minimum and maximum production rates, cash flows and NPV.     

Mine size optimization using marginal analysis

In this study, a model to estimate the optimum mine size is developed. The model is developed on the basis of marginal analysis. The model solves for the production rate at which the present value of marginal costs equals the present value of marginal revenues—the rate that microeconomic theory shows will maximize the net present value of production from the mine.In addition, the article discusses the effects on the optimum production rate of: the physical characteristics of the deposit, economic factors, and financial factors. It has been found that, not surprisingly, as the reserve tonnage increases, the optimum mine size increases. Also, the optimum production rate increases as the ore grade increases. A direct relationship has been found between the mineral price and the optimum production rate. The optimum mine size is found to be inversely related to the expected growth rate of mineral price, while it is directly related to the expected growth rate of mining costs. A concave relationship has been found between the cost of capital and the optimum mine size.     

Optimum cutting age for timber resources with carbon sequestration

Determining the optimum cutting age for timber resources has proved to be a very challenging problem for both economists and silviculturists. Based upon Samuelson's seminal work on this issue, the majority of economists have concluded that the optimum felling age occurs at a time when the net marginal benefits fall below the current rate of interest. Recently, concern about climate change has increased the importance of forestry projects, since trees act as natural biological scrubbers by removing CO₂ from the atmosphere. By incorporating these carbon sequestration benefits, this paper re-determines the optimum cutting age using a multiple rotation model. The results of this reformulation show that, in afforestation projects, trees should remain in the ground longer than the period suggested by a timber-only model in order to absorb more CO₂.     

An uncertainty based multi-criteria ranking system for open pit mining cut-off grade strategy selection

Cut-off grade strategy (COGS) is a concept that directly influences the financial, technical, economical, and environmental issues in relation to the exploitation of a mineral resource. Despite the simple definition of cut-off grade, the COGS problem is one of the complex and complicated problems in the mine planning process. From the optimization point of view, the COGS with an objective of maximizing the present value of future cash flows is a non-linear and a non-convex problem that even in its deterministic form can be solved using approximate optimization methods. This optimization problem will also be more complex and complicated under uncertainty conditions. This paper proposes an uncertainty based multi-criteria ranking system to investigate the problem of COGS selection considering metal price and geological uncertainties. The proposed system aims at selection of the best COGS among technically feasible alternative COGSs under uncertainty circumstances. Our developed system is based on integrating metal price and geological uncertainties as well as operating flexibility to close the mine early. We incorporate this operating flexibility into the proposed system using a Monte Carlo based real options (RO) valuation model. For this purpose, in addition to the expected value, other risk criteria are considered to rank the alternatives. These risk criteria include abilities of strategies in producing extra profits, minimizing losses, and achieving the predefined goals of the production. In this study, the technically possible COGSs are generated using the Lane comprehensive algorithm. To demonstrate the effectiveness of the proposed system, we utilize data of an Iranian gold mine. Results show that the proposed system outperforms conventional methods in the sense that it shows significantly lower average mis-ranking than the other methods and also selects a strategy with a higher value. The sensitivity analysis of the proposed system relative to the gold price shows that the system is highly dependent on the parameters of the stochastic process used to model the evolution of the metal price. Therefore, special consideration should be given in estimating stochastic process parameters.     

The choice of the cutoff grade in mining

In simple models, the cutoff grade has been shown to depend on the rate of growth of price net of the interest rate. But there is disagreement in the literature about whether the cutoff grade is positively or negatively related to this variable. In a model which involves two stages of production and a general grade distribution, we find that the rate of growth of price net of the interest rate has an influence, but that the sign of the effect is ambiguous because it depends on a complicated factor involving technical, mine-specific elasticities. This mine-specificity is consistent with the fact that engineering textbooks present the problem of optimal exploitation very simply, using a constant grade, and the fact that engineers use simulation in decision making. It also points to the possibility of moral hazard in exploitation, a possibility of potential concern to managers, shareholders and policy makers.     

Uncertainty in exhaustible natural resource economics: The irreversible sunk costs of Hotelling

According to Pindyck (2007) there are three important aspects of uncertainly in environmental economics: (1) the benefits and costs of environmental policy tend to be highly non-linear, (2) environmental policy tends to involve important irreversibilities, where investment in pollution abatement can impose an irreversible, sunk cost on society, and where certain pollutants can stay in the environment forever and build up to cause even more future harm in which case investment in abatement can cause an irreversible, sunk benefit to society, and (3) environmental policy involves long time horizons and yet the discount rate society should use is uncertain for determining the net present value of costs and benefits of pollution abatement. These same uncertainties also affect non-renewable, exhaustible, natural resource economics and in particular the use of the Hotelling rule: (1) the costs, benefits and transversality conditions of using the Hotelling rule can be highly non-linear, (2) the Hotelling rule involves important sunk cost irreversibilities, which will be explained here, and (3) the Hotelling rule can involve long time horizons with uncertain discount rates. All three of these problem make it extremely difficult for a market to use in any way the Hotelling rule, yet by the sheer number of articles in non-renewable natural resource economics, one would believe that it is the basis of all resource markets. In this article, we concentrate on the sunk cost irreversibilities of using the Hotelling rule. The idea of the Hotelling rule is to optimally store a non-renewable resource, but the optimization is highly dependent on the actual reserves that are available to extract. However, reserves of underground exhaustible resources are often unobservable at the beginning stages of extraction which makes using the Hotelling Rule difficult.     

Some observations on copper yields and ore grades

The paper examines trends in the average copper content of mined ores over the years. It has tended to decline over the long term, but by no means evenly. US averages are not typical of global averages, at least in the past four decades. Those have been both higher, and less volatile than in the US. One reason for falling averages is a change in the type of deposit mined, with a rise in the share of relatively low grade porphyry deposits. The different nature of their deposits is reflected in marked differences in grades between the different continents. African and Australian average grades are higher than the global average, and changes in the share of Central Africa in global output have affected the global average grade. Yields are have been consistently lower in North America than elsewhere, and Latin American average grades have trended downwards, reflecting both the ageing of mines and the rising share of production from porphyry deposits. Typically the yield of mines declines over time as mining proceeds. The average copper content of ore deposits is usually below the average yield of the ore accessed in the early years of production. The initial grades of new mines have not declined over the past forty years, and there has been no perceptible tendency for the average grade of porphyry deposits brought into production to decline over time. There is no apparent correlation between average grade and deposit size, but mine operators tend to exploit economies of scale to offset low grades. The relationship between the annual percentage yields (the head grade) and the reserve grades of deposits is not static. In recent years head grades have fallen closer to reserve grades. The relationship may be affected by movements in metal prices. Although the evidence about the influence of prices is not clear-cut, it does suggest that prices and cut-off grades may be inversely related. As many ores contain other valuable metals besides copper, copper yields will sometimes be subordinated to the extraction of these other metals. Copper equivalent grades have not moved in the same way as copper grades alone.     

农业资源开发规划优化与评估方法

本文把项目评估与农业资源开发规划模型的优化结合起来,用净现值法、益本比法和内部报酬率法进行项目评估,以净现值作为规划目标进行优化规划,并试用于泗阳县黄河故道滩区荒地资源开发的评估与规划,取得了显著的效果。     

Hydrologic analysis for coastal wetland restoration

Increasing recognition of the value of tidal wetlands has led to interest in how to restore and enhance areas that have been modified by human activity. The policy of recognizing restoration or enhancement as mitigation for destruction of other wetlands is controversial. Once policy questions are separated from technical questions, the steps in a successful project are straightforward A key element in the design of a successful project is quantitative hydraulic and hydrologic analysis of alternatives. Restoration projects at two sites in California used a combination of empirical geomorphic relationships, numerical modeling, and verification with field observations. Experience with these and other wetland restoration projects indicates the importance of longterm postproject monitoring, inspection, and maintenance     

AN ECONOMIC EVALUATION OF TWO WATERSHED MANAGEMENT PRACTICES IN TAIWAN1

ABSTRACT: The main purpose of this study is to evaluate the management practice effects on Ming-Hu and Ming-Tan reservoir watersheds during the past 15 years. It is difficult to economically evaluate a watershed project consisting of a number of multisectoral and long term management practices and regulations. However, the reservoirs’ hydropower operations and their associated benefits and costs are highlighted in this study. The estimated management practice value (net present value) of 351 million NT (New Taiwan) dollars and a benefit-cost ratio of 1.189 are obtained for the Ming-Hu subwatershed. Because the Ming-Tan hydropower station only began commercial operation in 1992 the estimated management practice value is negative 103 million NT dollars (net present value) and the benefit-cost ratio is 0.653 in the Ming-Tan subwatershed. If the analysis period is contained to the year 2010, the benefit-cost ratio of Ming-Tan reservoir subwatershed becomes 1.103. Ming-Hu and Ming-Tan subwatersheds together share the benefit-cost ratio of 1.182 and the net present value of 1,589 million NT dollars. The results of the analyses indicate that the Taiwan Power Company, the watershed management agency, has implemented economically efficient watershed practices and regulations in Ming-Hu and Ming-Tan reservoir watersheds and the watershed management practices are worthwhile and should be sustained.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.     

IRRIGATION PLANNING BASED ON WATER DEFICITS1

ABSTRACT: The deliberate underwatering of a larger land area, as practiced in Southern Asia, has provided impetus for a systematic investigation into the effects of designing projects for crop water deficits on Benefit-Cost performance. The study began with the derivation, from published experimental results, of functions relating ultimate crop yield to the magnitude and timing of water deficits, i.e., of the productivity of irrigation water. To obtain the net benefit of the project, the relation between the harvested area and output and the on-farm production costs was then suggested. The cost of supplying the irrigation water to the proposed area and of distributing and applying it to the field was determined, thus completing the Benefit-Cost equation. A computer simulation model was then established to search for the irrigation project design capacity and area to maximize the net present value in the Benefit-Cost analysis for the development proposed.     

OPTIMAL OPERATION OF SHELBYVILLE AND CARLYLE LAKES1

ABSTRACT: Dams were built by the U. S. Army Corps of Engineers on the Kaskaskia River at Shelbyville and Carlyle in Illinois, in 1969 and 1967, respectively. The operation of the Shelbyville and Carlyle Lakes has changed over the years because of considerably lower bankfull channel capacities downstream of the dams than were adopted in the project designs. This study was conducted to review the present operation policy. Intent was to derive a policy for maximizing the overall benefits (or minimizing the overall damages) and to compare these benefits or damages with those with the present policy. The operating rules were optimized through a simulation model which was structured considering the physical nature of the system and the desirable operation in the best interest of various beneficial uses. The expected annual value of overall benefits from recreation and agriculture is shown to increase by $0.2 million with the optimal policy. With the optimal operation, the overall damages are reduced by 76 percent on the average over the 24 years of flow record at Shelbyville and Carlyle.     

Benefit-cost analysis of spruce budworm (Choristoneura fumiferana Clem.) control: incorporating market and non-market values

This study employs a benefit-cost analysis framework to estimate market and non-market benefits and costs of controlling future spruce budworm (Choristoneura fumiferana) outbreaks on Crown forest lands in New Brunswick, Canada. We used: (i) an advanced timber supply model to project potential timber volume saved, timber value benefits, and costs of pest control efforts; and (ii) a recent contingent valuation method analysis that evaluated non-market benefits (i.e., changes in recreation opportunities and existence values) of controlling future spruce budworm outbreaks in the Province. A total of six alternative scenarios were evaluated, including two uncontrolled future budworm outbreak severities (moderate vs. severe) and, for each severity, three control program levels (protecting 10%, 20%, or 40% of the susceptible Crown land forest area). The economic criteria used to evaluate each scenario included benefit-cost ratios and net present values. Under severe outbreak conditions, results indicated that the highest benefit-cost ratio (4.04) occurred when protecting 10% (284,000 ha) of the susceptible area, and the highest net present value ($111 M) occurred when protecting 20% (568,000 ha) of the susceptible area. Under moderate outbreak conditions, the highest benefit-cost ratio (3.24) and net present value ($58.7 M) occurred when protecting 10% (284,000 ha) of the susceptible area. Inclusion of non-market values generally increased the benefit-cost ratios and net present values of the control programs, and in some cases, led to higher levels of control being supported. Results of this study highlight the importance of including non-market values into the decision making process of forest pest management.     

ESTIMATION OF OPTIMAL YIELD IN YUN-LIN AREA OF TAIWAN USING DECISION ANALYSIS1

ABSTRACT: Ground water is a vital resource in the Yun-Lin area of Taiwan. A substantial amount is continuously extracted, creating adverse effects such as land subsidence and seawater intrusion. Minimizing these negative impacts depends on regulating the rate of groundwater withdrawal. An optimal yield must be determined to establish a sound water management policy. A wide range of safe yields for Yun-Lin have already been proposed based on constant hydrological and hydrogeological parameters. By extending the results of those investigations, this study presents a decision analysis model. The optimal yield concept is introduced as well. The proposed model incorporates a probability density function for rainfall recharge and a loss function, derived from fluctuations in the ground water table. Through decision analysis, the optimum yield is obtained by minimizing the expected value of the loss function. The optimal yield varies monthly because the probability density function is time dependent. Analysis results suggest that the cumulative optimum yield of ground water in the area is 1.26 × 10⁸ m³/year. If the probability distribution function for rainfall recharge is modified as new precipitation data become available, the above suggested yield may require revision in the future.     

The role of price expectations and legal uncertainties in ocean mineral,exploration activities

In this paper, a standard exploration activities model is modified and applied to time series, data from deep seabed mining of a group of minerals where the number of patents is used as a proxy, for the level of mineral exploration activities. In addition to the rational expectations model, price, expectations formation for mineral prices is decomposed into trend and cyclical components using the, HP-filter method. Estimated parameters from the supply and cost functions are used to determine the, shadow price of the minerals. The non-linear instrumental variables estimator is employed to estimate, the exploration activities function. While the rational expectations model shows the importance of, current prices on exploration efforts, the HP-filter model suggests that firms concentrate on the trend, in prices rather than the short-run cyclical fluctuations. Also, while the U.S. refusal to ratify the LOSC, has increased the legal uncertainties surrounding the management of ocean resources and reduced the, incentive to engage in exploration activities, the passage of the ISA's main legislative accomplishment, regarding regulation of the explorations for polymetallic nodules appear to have made a positive effect.     

Manganese nodules— an example of a Lasky distribution?

Readily accessible analytical data from 530 stations from which manganese nodules have been collected are used to investigate what relationship, if any, there is between grade (expressed as the combined copper and nickel content) and the number of samples. It is concluded that not only average grade but also cut-off grade have the relationships with cumulative quantities suggested by Lasky, subject to the exclusion of certain, apparently anomalous, data. These relationships can be used to derive information on the distribution of the quantity of contained metal at different average and cut-off grades, which may have applications to other mineral deposits.     

Evaluating mine plans under uncertainty: Can the real options make a difference?

Over the last few years, many studies have presented the real options valuation (ROV) as a promising technique of valuing natural resource investments under conditions of uncertainty. Apart from the common conclusion that the ROV is better than the conventional net present value (NPV) method in integrating the value of management flexibility and proper handling of cash flows risk, there is a lack of procedures for testing the usefulness and advantages of the ROV over the static NPV method in practice. Arguably, it is not yet clear whether the ROV can deal with the complexity of mining projects and whether it can really be applied to make decisions that improve project value.     

Statistical considerations of progressive value and risk in mineral exploration

Financial markets recognise maximisation of expected value (E), in an essentially risk-neutral context, as the main corporate financial objective of private enterprise. This may be valid for large, integrated mining companies. Yet, most junior and middle-size exploration companies behave in a risk-averse fashion when making decisions about progressively more expensive exploration programs. From their perspective, a potential increase in expected value from either an increase in target value or related probability of discovery, or both, may not be a sufficient incentive to embark in an exploration programme if the resultant increase in expected value is accompanied by a significant increase in possible maximum loss. Risk-averse explorers may be unwilling to bear larger, albeit less probable losses, when the cost of successive exploration programmes is taken into account. The paper provides a practical methodology for such explorers to optimise the decision whether to progress to the next stage of exploration or to farm out a risky project. It uses a decision-tree model incorporating the effectiveness of the proposed exploration programme, the explorer's risk tolerance and related utility values and the probability distribution of the possible value of the exploration target.     

生态产品价值实现的“一村万树”绿色期权模式

随着经济的不断发展，越来越多的国家和地区开始重视绿色高质量发展，对生态产品的研究也在不断加强。各种政策工具相继出现，致力于将自然给予的生态产品资本化，并赋能经济发展。其中，衢州市柯城区的“一村万树”项目就是一种具有创新性的生态产品价值实现模式。本文对衢州市柯城区“一村万树”项目及其绿色期权模式进行研究，结合部门统计数据和空间信息数据，对“一村万树”项目实施区2018年的生态效益进行核算，并选取柯城区2010—2018年相关社会经济统计数据进行相关性分析，探析项目的社会经济效益，最后在量化分析的基础上结合公共池塘资源治理的八条设计原则，定性分析了“一村万树”绿色期权的合理性。结果显示：“一村万树”实施区2018年的生态效益为124.63亿元，约为研究区国内生产总值估算值的1.68倍，说明该项目具有巨大的生态效益；同时，相关分析结果表明该项目实施对当地第三产业的发展有较大的促进作用。柯城区“一村万树”项目以及绿色期权模式给当地带来了巨大的生态和社会经济效益，为我国的乡村绿化建设和生态产品价值实现提供了一种新范式。