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.     

Determination of the effect of operating cost uncertainty on mining project evaluation

Mining projects are complex businesses that demand constant risk assessment. This is because several kinds of uncertainties influence the value of a mine project, typically. These uncertainties may be classified as exploration uncertainties, economic uncertainties and engineering uncertainties. The evaluation of a mine project under these uncertainties is a complicated job, which may lead to making a wrong decision by managers and stockholders. Therefore, at first, the engineers must recognize the mining uncertainties before carrying out the project evaluation. The economic uncertainties are the most important factors, which may affect the project evaluation. Among the mentioned uncertainties, the operating cost uncertainty is an important and effective factor, which is ignored to a certain extent.     

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

Evaluating a small deposit next to an economically viable gold mine in West Africa from the points of view of the mining company,the government and the local community

This paper addresses the question of evaluating how much the different stakeholders stand to gain from a mining project. By carefully analysing the breakdown of the cash-flows generated, we were able to estimate the amounts received by the local community and by the national community (outside the mining area), the taxes and royalties received by the government and the profits made by the mining company. A real options framework was used to take account of the inherent uncertainty on the commodity price and the reserves, and the operating flexibility (that is, the possibility for the company to stop mining if the commodity price drops and/or the reserves prove to be lower than that had been envisaged). A synthetic case-study of a gold mine in West Africa was used to illustrate how this procedure could be applied in practice. By using the real option framework we were able to envisage scenarios for developing an extension to a deposit as a function of future values of the commodity price. The procedure proposed should provide governments and NGOs with more objective data for making policy decisions.     

Optimal production and pricing policy for a closed loop system

A closed loop system is investigated, in which the manufacturer has two channels to satisfy the demand: manufacturing brand-new products and remanufacturing returns into as-new products. Remanufactured products have no difference from brand-new products and can be sold in the same market at the same price. The demand is uncertain and sensitive to the selling price, while the return is also stochastic and sensitive to the acquisition price of used products. A mathematical model is developed to maximize the overall profit of the system by simultaneously determining the selling price, the production quantities for brand-new products and remanufactured products, and the acquisition price of used products. Some properties of the problem are analyzed, based on which a solution procedure is presented. Through a numerical example, the impacts of the uncertainties of both demand and return on the production plan, selling price, and the acquisition price of used products are analyzed.     

Gold demand and supply

Western mine production of gold has been declining in the past five years — at the same time as the price of gold has risen dramatically. Predictions of a continued high demand for gold and the current US interest in adopting some form of ‘gold standard’ have focused attention on the supply of new gold. This paper discusses the structure of gold supply and demand, the present pattern of production of new gold and the possible effect of future price changes on Western gold mine production in the 1980s.     

IFRP: a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

In this study, an interval-parameter fuzzy-robust programming (IFRP) model is developed and applied to the planning of solid waste management systems under uncertainty. As an extension of the existing fuzzy-robust programming and interval-parameter linear programming methods, the IFRP can explicitly address system uncertainties with complex presentations. Parameters in the IFRP model can be represented as interval numbers and/or fuzzy membership functions, such that the uncertainties can be directly communicated into the optimization process and resulting solution. Furthermore, highly uncertain information for the lower and upper bounds of interval parameters that exist due to the complexity of the real world can be effectively handled through introducing the concept of fuzzy boundary interval. Consequently, robustness of the optimization process and solution can be enhanced. Results of the case study indicate that useful solutions for planning municipal solid waste management practices can be generated. They reflect a compromise between optimality and stability of the study system. Willingness to pay higher costs will guarantee the system stability; however, a desire to reduce the costs will run the risk of potential instability of the system. The results also suggest that the proposed hybrid methodology is applicable to practical problems that are associated with highly complex and uncertain information.     

Evaluating the impact of uncertainty and variability on the value chain optimization of a forest biomass power plant using Monte Carlo Simulation

Mathematical programming models have been used to optimize the design and management of forest bioenergy supply chains. A deterministic mathematical model is beneficial for making optimum decisions; however, its applicability to real-world problems may be limited because it does not capture all the complexities, including uncertainties in the parameters, in the supply chain. In this paper, a combination of Monte Carlo Simulation and optimization model is used to evaluate the impact of uncertainty in biomass quality, availability and cost, and electricity prices on the supply chain of a forest biomass power plant. The optimization model is a deterministic mixed integer non-linear model with monthly time steps over a 1-year planning horizon. Variability in biomass quality, i.e. moisture content (MC) and higher heating value (HHV), based on the historical data of a real case study is studied in detail and fitted probability distributions are used in the model, while for electricity prices different scenarios are considered. The results show that the impact of variability in the MC on profit is higher than that of uncertainty in HHV. It is observed that the annual profit ranges between $13.3 million and $17.9 million in the presence of all possible uncertainties while its average is $15.5 million. Uncertainty in biomass availability and cost and electricity price results in the risks of having annual profit of less than $14 million and low monthly storage levels.     

Two-stage planning for sustainable water-quality management under uncertainty

In water-quality management problems, uncertainties may exist in a number of impact factors and pollution-related processes (e.g., the volume and strength of industrial wastewater and their variations can be presented as random events through identifying a statistical distribution for each source); moreover, nonlinear relationships may exist among many system components (e.g., cost parameters may be functions of wastewater-discharge levels). In this study, an inexact two-stage stochastic quadratic programming (ITQP) method is developed for water-quality management under uncertainty. It is a hybrid of inexact quadratic programming (IQP) and two-stage stochastic programming (TSP) methods. The developed ITQP can handle not only uncertainties expressed as probability distributions and interval values but also nonlinearities in the objective function. It can be used for analyzing various scenarios that are associated with different levels of economic penalties or opportunity losses caused by improper policies. The ITQP is applied to a case of water-quality management to deal with uncertainties presented in terms of probabilities and intervals and to reflect dynamic interactions between pollutant loading and water quality. Interactive and derivative algorithms are employed for solving the ITQP model. The solutions are presented as combinations of deterministic, interval and distributional information, and can thus facilitate communications for different forms of uncertainties. They are helpful for managers in not only making decisions regarding wastewater discharge but also gaining insight into the tradeoff between the system benefit and the environmental requirement.     

试论长江上游砂金矿成矿地质特征及开发

砂金是黄金的重要来源之一,一般认为砂金矿的形成和富集主要与三四级水系密切,而不重视一二级水系,认为不易形成砂金矿.近2年来,经地质调查和研究发现在长江上游一级水系中富集有砂金矿。砂金主要赋存于第四系冲积层内,砂砾层中普遍含金,品位较高,埋藏浅,有利于开采;成矿条件较好,具有一定远景储量。     

不确定条件下矿产资源的最优开采

通过一个连续时间的随机动态规划模型,探讨了市场需求、资源存量的不确定性以及勘探活动对矿产资源价格和开采速度的影响,并给出了随机条件下Hotelling法则的表达形式.模型结果显示:不确定性对资源价格变化速度的影响主要取决于开采成本,如果相对于资源存量来说开采成本是不变的或者开采的规模成本是不变的,则不确定性对资源价格的变化速度没有影响.反之,如果开采的规模成本是递增的,则不确定性会加速资源价格的变化.此外,不确定性的存在将加快资源的开采速度.至于勘探活动,它一方面降低了地质条件的不确定性,另一方面增加了资源的存量,所以勘探活动降低了资源价格和开采速度的变化率,减少了不确定性对资源开采的影响.     

Inexact multistage stochastic integer programming for water resources management under uncertainty

In this study, an inexact multistage stochastic integer programming (IMSIP) method is developed for water resources management under uncertainty. This method incorporates techniques of inexact optimization and multistage stochastic programming within an integer programming framework. It can deal with uncertainties expressed as both probabilities and discrete intervals, and reflect the dynamics in terms of decisions for water allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the IMSIP can facilitate analyses of the multiple policy scenarios that are associated with economic penalties when the promised targets are violated as well as the economies-of-scale in the costs for surplus water diversion. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that reasonable solutions have been generated for both binary and continuous variables. For all scenarios under consideration, corrective actions can be undertaken dynamically under various pre-regulated policies and can thus help minimize the penalties and costs. The IMSIP can help water resources managers to identify desired system designs against water shortage and for flood control with maximized economic benefit and minimized system-failure risk.     

An Optimization Method Based on Scenario Analysis for Watershed Management Under Uncertainty

In conjunction with socioeconomic development in watersheds, increasingly challenging problems, such as scarcity of water resources and environmental deterioration, have arisen. Watershed management is a useful tool for dealing with these issues and maintaining sustainable development at the watershed scale. The complex and uncertain characteristics of watershed systems have a great impact on decisions about countermeasures and other techniques that will be applied in the future. An optimization method based on scenario analysis is proposed in this paper as a means of handling watershed management under uncertainty. This method integrates system analysis, forecast methods, and scenario analysis, as well as the contributions of stakeholders and experts, into a comprehensive framework. The proposed method comprises four steps: system analyses, a listing of potential engineering techniques and countermeasures, scenario analyses, and the optimal selection of countermeasures and engineering techniques. The proposed method was applied to the case of the Lake Qionghai watershed in southwestern China, and the results are reported in this paper. This case study demonstrates that the proposed method can be used to deal efficiently with uncertainties at the watershed level. Moreover, this method takes into consideration the interests of different groups, which is crucial for successful watershed management. In particular, social, economic, environmental, and resource systems are all considered in order to improve the applicability of the method. In short, the optimization method based on scenario analysis proposed here is a valuable tool for watershed management.     

Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints

The existing inexact optimization methods based on interval-parameter linear programming can hardly address problems where coefficients in objective functions are subject to dual uncertainties. In this study, a superiority–inferiority-based inexact fuzzy two-stage mixed-integer linear programming (SI-IFTMILP) model was developed for supporting municipal solid waste management under uncertainty. The developed SI-IFTMILP approach is capable of tackling dual uncertainties presented as fuzzy boundary intervals (FuBIs) in not only constraints, but also objective functions. Uncertainties expressed as a combination of intervals and random variables could also be explicitly reflected. An algorithm with high computational efficiency was provided to solve SI-IFTMILP. SI-IFTMILP was then applied to a long-term waste management case to demonstrate its applicability. Useful interval solutions were obtained. SI-IFTMILP could help generate dynamic facility-expansion and waste-allocation plans, as well as provide corrective actions when anticipated waste management plans are violated. It could also greatly reduce system-violation risk and enhance system robustness through examining two sets of penalties resulting from variations in fuzziness and randomness. Moreover, four possible alternative models were formulated to solve the same problem; solutions from them were then compared with those from SI-IFTMILP. The results indicate that SI-IFTMILP could provide more reliable solutions than the alternatives.     

TMDL中MOS的定量估算方法及其应用

为了分析TMDL水污染控制管理模式中安全临界值MOS的影响因素,采用FOEA法对MOS中模拟计算的不确定性进行定量估算,通过不同水质达标率条件下MOS的设定,探讨水环境管理中不确定性因素对MOS的影响;将TMDL应用于珠江三角洲佛山水道的水环境管理中,运用动态水环境数学模型、考虑潮周期达标率的环境容量优化模型及遗传算法对TMDL进行求解.研究结果表明,所采用的FOEA法能较为准确地反映模型的不确定性对MOS的影响,而且从水质达标率的角度出发能合理地考察环境管理中的不确定性因素对MOS的影响,为定量化探讨MOS的设定给出了可行的求解思路及方法.     

An overview of global gold market and gold price forecasting

The global gold market has recently attracted a lot of attention and the price of gold is relatively higher than its historical trend. For mining companies to mitigate risk and uncertainty in gold price fluctuations, make hedging, future investment and evaluation decisions, depend on forecasting future price trends. The first section of this paper reviews the world gold market and the historical trend of gold prices from January 1968 to December 2008. This is followed by an investigation into the relationship between gold price and other key influencing variables, such as oil price and global inflation over the last 40 years. The second section applies a modified econometric version of the long-term trend reverting jump and dip diffusion model for forecasting natural-resource commodity prices. This method addresses the deficiencies of previous models, such as jumps and dips as parameters and unit root test for long-term trends. The model proposes that historical data of mineral commodities have three terms to demonstrate fluctuation of prices: a long-term trend reversion component, a diffusion component and a jump or dip component. The model calculates each term individually to estimate future prices of mineral commodities. The study validates the model and estimates the gold price for the next 10 years, based on monthly historical data of nominal gold price.     

Two-stage vertex analysis method for planning electric power systems with greenhouse gas abatement consideration

This study presents a two-stage vertex analysis (TSVA) method for the planning of electric power systems (EPS) under uncertainty. TSVA has advantages in comparison to other optimization techniques. Firstly, TSVA can incorporate greenhouse gas (GHG) abatement policies directly into its optimization process, and, secondly, it can readily integrate inherent system uncertainties expressed as fuzzy sets and probability distributions directly into its modeling formulation and solution procedure. The TSVA method is applied to a case study of planning EPS and it is demonstrated how the TSVA efficiently identify optimal electricity-generation schemes that could help to minimize system cost under different GHG-abatement considerations. Different combinative considerations on the uncertain inputs lead to varied system costs and GHG emissions. Results reveal that the total electricity supply will rise up along with the time period due to the increasing demand and, at the same time, more non-fossil fuels should be used to satisfy the increasing requirement for GHG mitigation. Moreover, uncertainties in connection with complexities in terms of information quality (e.g., capacity, efficiency, and demand) result in changed electricity-generation patterns, GHG-abatement amounts, as well as system costs. Minimax regret (MMR) analysis technique is employed to identify desired alternative that reflects compromises between system cost and system-failure risk.     

Risk-based evaluation of wastewater treatment projects: A case study in Niasar city,Iran

For sustainable wastewater management, it is essential to consider social, environmental, geological and technical features as well as economic feature in the decision-making process. A limitation of many of the earlier works on wastewater management is that they take into account only financial criteria to make a decision for a given problem. Moreover, the decision-makers’ (DMs) attitude to risk, or optimism degree, when faced with uncertainty is not considered. In this paper, we study the application of risk-based multi-attribute decision-making (RB-MADM) methods to achieve sustainable wastewater management. Consideration of uncertainty, value tradeoffs, and different risk attitudes of decision makers are the important features of the developed methodology. A case study on the Iranian city of Niasar is presented to illustrate how this methodology can be applied to select the most preferred alternative for wastewater management among a set of options. The most preferred option is selected with respect to nine attributes under different optimism/pessimism degrees, using six different MADM methods. The results show that the ranking of options is sensitive to the optimism degree of the DMs. The proposed approach may help policy makers to achieve sustainable wastewater management.     

Applying Zonation Methods and Tabu Search to Improve the Ground‐Water Modeling1

Abstract: An optimization procedure combining zonation methods with the Tabu Search method is proposed to identify the spatial distribution of hydraulic conductivity field. Three zonation methods, Voronoi diagram (VD), multiplicatively weighted Voronoi diagram (MWVD), and pattern zonation are adopted for the parameterization purposes. With the consideration of the homogeneity and the heterogeneity, there are four spatial distributions of hydraulic conductivity designed to test whether the parameter structure can be successfully identified. The fitting residual error is first considered to determine an adequate number of zones without over parameterization. Then, the parameter uncertainty is evaluated the decision of the number of zones. The results indicate that the MWVD performs better than other two methods because the MWVD has better flexibility in describing the zonal boundaries with small number of decision variables.