露天矿边际品位最优化的经济分析
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摘要
矿石开采边际品位的确定是矿产业中一个非常重要的决策问题，它一方面直接影响到矿山企业经济效益高低，同时还影响整个国家的矿产资源有效利用的水平。矿石开采边际品位的确定涉及到复杂的分析与计算，它与经济管理、地质、采矿、选矿、应用数学、计算机等学科知识紧密相联系。虽然先前的矿业工程经济与管理学者在这一领域做了许多卓有成效的研究，然而目前仍然存在大量的问题有待探索。本论文研究露天矿开采边际品位经济最优化的理论方法及其数学模型问题。
本文的主要内容和研究成果如下：
(1)对国内外关于矿石开采品位指标经济分析问题研究的思想方法演进做了较详尽的分析与评论，并根据经济分析方法的典型特征进行了历史阶段的分期。对矿石开采品位指标体系问题进行了探讨，认为我国必须从双指标体系转变到单指标体系。深入地剖析了影响矿石开采边际品位经济性分析的主要技术经济因素，为最优化建模提供了变量关联性分析基础。(2)对西方国家比较成熟的露天矿边际品位最优化的边际分析法模型结构进行了系统地考察、剖析与评价，从而可以更深刻地认识其优化的经济特征及局限性。(3)在现代资源经济学的启示之下，运用控制理论建立了露天矿边际品位最优化模型，其数学结构化程度比边际分析法显著地提高了一步，它还能为矿山开采决策提供更多的信息。(4)针对矿产品市场的高度波动性，引入实物期权理论研究边际品位最优化问题。通过连续参量期权定价模型，建立了服务年限无穷大时边际品位依价格波动而连续调整下的矿山价值决定的偏微分方程，并获得其解析解：用蒙托卡洛模拟分析了有限服务年限下价格呈平均回弹过程的边际品位最优调整问题，结果表明在期权理论指导下的品位调整策略，反映出矿石开采决策的随机、动态特征，它比现行的品位策略理论在分析上更为全面、深入，从而能为矿山带来更多的价值。(5)针对矿山开采实践的复杂性，综合地运用
管理经济学中各种决策成本理论，建立了准优化模型。这类模型建模
过程简单，计算方便，对我国的生产矿山进行低品位矿利用分析具有
优越性。(6)以国民经济效益优化为目标，研究了相应的边际品位的
确定及其矿山开采边际品位决策行为的宏观调控问题。(7)论文相应
部份中对其所提出的主要模型进行了案例分析，以展示新建模型的功
能优势。
本文除对上述各部分进行了经济分析和模型创新之外，并注意力
求在整体上构成一个有机的逻辑框架，以系统地展示露天矿边际品位
最优化经济分析的理论方法与模型。
The determination of cutoff grade in mining operation is an important decision-making problem. On one hand, it directly affects the profitability of a mine. On the other hand, it has great impact on the efficiency of mineral resource utilization of a whole nation. The determination of cutoff grade involves complicated analysis and calculations, and it has close relations with the knowledge of geology, mining, mineral processing, applied mathematics, economics and management. Although a lot of successful researches in this field have been done by many mineral engineering economists, there are still tremendous research opportunities exist at present. This dissertation focuses on the study of economic analysis and mathematical models of open pit cutoff grade optimization. The contents and research results of this dissertation are as follows.
(l)The evolution of the theories and models of cutoff grade both in China and abroad is described, historical time period is determined according to their analytical method. The cutoff grade systems are discussed, and it proposes that China should change from dual cutoff grade system to a single one. The technological and economic factors relating to the cutoff grad analysis are studied, providing the basis for the inter-variable relations analysis in optimization modeling; (2)A deep examination of the structure of open pit cutoff grade optimization based marginal analysis, is made, so that we can have a thorough understanding of economic character and limits of this theory; (3)The mathematical model of open pit cutoff grade optimization based on the application of control theory is established. This model is enlightened by modern resource economics. The model is of higher grade in terms of mathematical structure. It also provides more information for mine decision makers; (4)In order to deal with the highly
uncertain mineral product prices, the option pricing theory is introduced. A partial differential equation is constructed for the measuring of a mine's value
IV
with cutoff grade flexibility under the assumption of permanent mine life. A Mont Carlo simulation system is established for a mine with limited mine life and its product price following mean-reverting process. The results shows that the cutoff grade strategy under the guidance of option pricing theory can obtain more value for a mine; (5)The second best models of cutoff grade determination is studies. The model is suitable for the cases that grade distribution function is not available or the ore reserve is hard to estimate. This kind of models can be easily constructed. They are especially applicable for the economic analysis of the utilization of low-grade ores in China; (6)The macroeconomics of cutoff grade is discussed, and the ways of macro adjustment of mining behavior is analyzed.In each relevant part, the numerical case studies or practical applications are presented.
Besides the above-mentioned discussions and mathematical model construction in each part, this dissertation also constructed a systematic logical framework that demonstrates the theory, methodology and models of the economic analysis of open pit cutoff grade optimization.
本文的主要内容和研究成果如下：
(1)对国内外关于矿石开采品位指标经济分析问题研究的思想方法演进做了较详尽的分析与评论，并根据经济分析方法的典型特征进行了历史阶段的分期。对矿石开采品位指标体系问题进行了探讨，认为我国必须从双指标体系转变到单指标体系。深入地剖析了影响矿石开采边际品位经济性分析的主要技术经济因素，为最优化建模提供了变量关联性分析基础。(2)对西方国家比较成熟的露天矿边际品位最优化的边际分析法模型结构进行了系统地考察、剖析与评价，从而可以更深刻地认识其优化的经济特征及局限性。(3)在现代资源经济学的启示之下，运用控制理论建立了露天矿边际品位最优化模型，其数学结构化程度比边际分析法显著地提高了一步，它还能为矿山开采决策提供更多的信息。(4)针对矿产品市场的高度波动性，引入实物期权理论研究边际品位最优化问题。通过连续参量期权定价模型，建立了服务年限无穷大时边际品位依价格波动而连续调整下的矿山价值决定的偏微分方程，并获得其解析解：用蒙托卡洛模拟分析了有限服务年限下价格呈平均回弹过程的边际品位最优调整问题，结果表明在期权理论指导下的品位调整策略，反映出矿石开采决策的随机、动态特征，它比现行的品位策略理论在分析上更为全面、深入，从而能为矿山带来更多的价值。(5)针对矿山开采实践的复杂性，综合地运用
管理经济学中各种决策成本理论，建立了准优化模型。这类模型建模
过程简单，计算方便，对我国的生产矿山进行低品位矿利用分析具有
优越性。(6)以国民经济效益优化为目标，研究了相应的边际品位的
确定及其矿山开采边际品位决策行为的宏观调控问题。(7)论文相应
部份中对其所提出的主要模型进行了案例分析，以展示新建模型的功
能优势。
本文除对上述各部分进行了经济分析和模型创新之外，并注意力
求在整体上构成一个有机的逻辑框架，以系统地展示露天矿边际品位
最优化经济分析的理论方法与模型。
The determination of cutoff grade in mining operation is an important decision-making problem. On one hand, it directly affects the profitability of a mine. On the other hand, it has great impact on the efficiency of mineral resource utilization of a whole nation. The determination of cutoff grade involves complicated analysis and calculations, and it has close relations with the knowledge of geology, mining, mineral processing, applied mathematics, economics and management. Although a lot of successful researches in this field have been done by many mineral engineering economists, there are still tremendous research opportunities exist at present. This dissertation focuses on the study of economic analysis and mathematical models of open pit cutoff grade optimization. The contents and research results of this dissertation are as follows.
(l)The evolution of the theories and models of cutoff grade both in China and abroad is described, historical time period is determined according to their analytical method. The cutoff grade systems are discussed, and it proposes that China should change from dual cutoff grade system to a single one. The technological and economic factors relating to the cutoff grad analysis are studied, providing the basis for the inter-variable relations analysis in optimization modeling; (2)A deep examination of the structure of open pit cutoff grade optimization based marginal analysis, is made, so that we can have a thorough understanding of economic character and limits of this theory; (3)The mathematical model of open pit cutoff grade optimization based on the application of control theory is established. This model is enlightened by modern resource economics. The model is of higher grade in terms of mathematical structure. It also provides more information for mine decision makers; (4)In order to deal with the highly
uncertain mineral product prices, the option pricing theory is introduced. A partial differential equation is constructed for the measuring of a mine's value
IV
with cutoff grade flexibility under the assumption of permanent mine life. A Mont Carlo simulation system is established for a mine with limited mine life and its product price following mean-reverting process. The results shows that the cutoff grade strategy under the guidance of option pricing theory can obtain more value for a mine; (5)The second best models of cutoff grade determination is studies. The model is suitable for the cases that grade distribution function is not available or the ore reserve is hard to estimate. This kind of models can be easily constructed. They are especially applicable for the economic analysis of the utilization of low-grade ores in China; (6)The macroeconomics of cutoff grade is discussed, and the ways of macro adjustment of mining behavior is analyzed.In each relevant part, the numerical case studies or practical applications are presented.
Besides the above-mentioned discussions and mathematical model construction in each part, this dissertation also constructed a systematic logical framework that demonstrates the theory, methodology and models of the economic analysis of open pit cutoff grade optimization.
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