地下开采边界品位动态优化研究及其应用
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摘要
在矿山开采过程中,边界品位是最基本、最重要的参数之一。边界品位的选择直接影响所圈定矿体的形态及矿石储量,进而影响矿山建设、生产规模、收益、设备选择和生产寿命,同时还影响到不可再生资源的利用率。因此,边界品位是一个对矿山经济效益和社会效益有着重大影响的技术经济参数。边界品位的优化,也是矿山经营参数优化的核心内容之一。
国内外在边界品位研究中经历了50多年的历史,尽管做出了许多非常有价值的成果,但还存在不足：盈亏平衡法得到的边界品位,是一个与矿石质量、时间和位置无关的静态区分标准,没有考虑资金的时间价值,它的不合理性是显而易见的,这种方法逐渐被淘汰；最大现值法是假设整个优化范围的品位服从同一统计学分布,即这一分布在该范围是处处相同。在这个假设条件下,得到使总净现值最大的优化结果是边界品位逐年下降。现实中几乎所有矿床都不满足这一假设条件,矿床一般都有高品位区和低品位区。当低品位区位于矿床的上部时,开始一个时期采用高的边界品位显然是不合理的,甚至是无法实现的。因此,要得到符合实际的最优边界品位,必须考虑矿床不同区段的真实品位分布。
针对边界品位优化研究中存在的问题,在研究地下开采工艺的基础上,根据矿床的赋存条件和矿体的开采顺序,把优化范围划分为一系列的区段,即优化单元。在此基础上,将开采过程分成前后过渡的开采阶段,每个开采阶段包括若干个状态,一个阶段的一个状态由从开始到该阶段开采完毕的累积开采矿量作为状态变量,一个阶段的一个状态对应的开采矿量是从过渡到该状态的前一阶段某状态的累积矿量和本状态的累积矿量求的。开采方案从第一阶段的各状态开始,从优化单元1的品位—矿量曲线上得到各状态矿量对应的边界品位,根据开采过程中发生的投资与使用的采矿方法所发生的生产成本计算出开采矿量所得的赢利,再根据矿山的年生产能力计算出开采时间,并将赢利折现到开采初期时的净现值。这样第一阶段完成后,就得到该阶段各状态的矿量、边界品位和净现值。第二阶段各状态是由第一阶段的某些状态过渡而来。以第二阶段的某个状态为例,假设第一阶段中有k个状态可以过渡到该状态,每个过渡都有一个本阶段开采的矿量,这个矿量是在优化单元2开采的,从第二优化单元的品位—矿量曲线可以得到这一矿量对应的边界品位值、获得的利润以及该利润折现到开采初期时的净现值。该状态的净现值就等于过渡到该状态的前一阶段状态的净现值加上开采矿量获得利润通过折现后的净现值,从前阶段的k个状态过渡到本阶段有k个不同的净现值,该状态的净现值取这k个不同净现值中的最大者,而该状态的边界品位就是获得最大净现值时对应的边界品位。用同样的方法一直计算到最后阶段(最后一个优化单元)每个状态的净现值和边界品位。从最后阶段的各状态中找出净现值最大的状态,按过渡的顺序反推回去,就得到每个阶段的最优过渡(也叫最优决策),这些最优决策组成该边界品位优化问题的最优解。根据上述优化思路,建立了新的动态规划边界品位优化模型。该模型以净现值为指标函数,同时考虑矿体的开采顺序、矿山的年生产能力以及矿石品位在不同区段(优化单元)的实际分布,并与实际使用的采矿方法相结合。该模型实现了地下开采边界品位优化在时间上与空间上的动态结合,在地下开采边界品位优化方法的一次突破。
论文还基于Lane法的思路,分析地下开采和露天开采的不同特点,推导出采矿、选矿两阶段和采矿、选矿、冶炼三阶段的地下开采边界品位优化数学模型。模型增加了贫化率和围岩品位等参数,引用围岩品位与矿石地质品位比值的变量,使之适用于地下矿山。
基于两种优化方法的数学模型,开发了相应的计算机软件系统：动态规划优化系统(DPOS1.0)和矿山经济决策系统(MEDS1.0)。DPOS1.0不仅可以求得各优化单元的开采矿量、边界品位、累计的生产年限以及现值等结果,还可以通过动态规划网络图,直观的得到各优化单元之间有效的决策集合和该优化问题的最优策略。MEDS1.0不仅可以对整个矿体作为优化对象,还可以选取任意勘探线和水平之间的范围作为优化对象,同时能够使用多套经济技术参数方案,弥补了传统现值法假设优化范围品位分布不变的局限性。该系统是基于谦比西铜矿开发的,但也可以应用于其他同类矿山,是一个相对通用的矿山经济决策软件。
这一边界品位动态优化方法应用于赞比亚谦比西铜矿,对崩落法开采的两个阶段的边界品位进行了优化。动态优化法将优化范围划分为12个优化单元(动态规划的阶段),每个优化单元有自己的品位分布,按照一定的开采顺序。优化的结果是：优化单元1到12的边界品位和开采矿量分别是1.004%和853823.852吨、0.808%和1333158.948吨、0.905%和913919.33吨、1.002%和883214.087吨、1.015%和906692.185吨、0.999%和965396.035吨、0.995%和716111.732吨、1.007%和708986.005吨、0.993%和710850.398吨、0.993%和759790.244吨、0.993%和709781.188吨、0.989%和740540.653吨,共开采矿石10202264.66吨,开采时间近10年,最大现值为24281.68万美元,边界品位优化结果在0.808%至1.015%之间。按照目前矿山使用的边界品位1%计算,共开采矿量9719937.8吨,开采时间9年5个月,最大现值为23891.76万美元。
Cutoff grade is one of the most basic and important parameters in mining process. The selection of cutoff grade affects the shape of the enclosed ore-body and ore reserves directly, and then affects mine construction, scale of production, income of mine, facilities selection, and production life-span, and even utilization rate of non-renewable resource. Therefore, cutoff grade is a major impact on the technical and economic parameters both in mine economic benefits and social benefits. Cutoff grade optimization is also one of the core content in mine management parameters' optimization.
Scholars of domestic and foreign had made many valuable achievements about cutoff grade studies in the last 50 years,but it had the following insufficiencies:Cutoff grade which is defined by the profit and loss balance Method,is one static discrimination standard,which has nothing to do with the ore quality, the time and the position,and it don't considere the time value. Inconsequence of this method is obviously, therefore it is eliminated gradually. The Maximum NPV Method supposes that cutoff grade in entire optimization scope obediences identical statistics distribution, that is to say, this distribution is identical everywhere in this scope. Under this hypothesis, optimized result that make the total NPV maximum is that cutoff grade decreased year by year. But in practice, almost all deposits don't meet this hypothetical condition, and they generally have low-grade and high-grade areas. When the low-grade area was located at the upside of the deposit, mining process by a high cutoff grade is obviously unreasonable and even impossible to achieve. In order to obtain the optimal cutoff grade that accords with the actual practice, we must consider the actual grade distribution in the different sections of the deposit.
Aiming at the insufficiencies of the cutoff grade optimization studies, basing on the research of underground mining technology, and according to the mineral deposit conditions and ore mining sequence, the optimization scope was divided into a series of sections, namely optimize units. On this basis, the mining process is divided into transition mining stage of the before and after,and a stage include a number of states.The state variable of a stage was showed by cumulate mining quantity from start to this stage mining finished. Mining quantity of a state in a stage is gained from cumulate mining quantity of the state in this stage and cumulate mining quantity of the transition state of preceding stage.The mining scheme begins from each states of the first stage. Cutoff grade of every state could be obtained from the graph of distribution and grade VS mine quantity of optimize unit-1.Profit of mining quantity could be calculated by the investment of mining process and the cost of mining by the corresponding mining method. Then, according to the annual production capacity of mine, the production life-span could be calculated, and the profit could convert into the NPV of initial stage. After the first stage, mining quantity, cutoff grade and NPV of each state of this stage could be obtained. Every state of the second stage was come from certain state of the first stage. Taking one state of the second stage as an example, supposing that this state could be transited by K states in the first stage and every transition has a mining quantity which is mined in optimize unit-2. So the cutoff grade, the profit and its NPV(discount to initial stage) can be obtained from the graph of distribution and grade VS mine quantity of optimize unit-2. NPV of this state is equal to that NPV of the former transition state add on NPV obtained by the mining quantity. NPV of this state was maximal one among the K-NPVs which come from the K-states of former stage. And the cutoff grade of this state was the one which corresponds with the maximum NPV.The cutoff grade and the NPV of each state were calculated to the final stage (final optimize unit) with similar method. Find out the having maximum NPV of the state in last stage and deduced by reverse sequence of the transition order, then the optimal transition (also called optimal decision-making) of every stage was obtained. The optimal result of this cutoff grade optimization problem was composed of all optimal decision-makings. According to the above optimization ideas, a new dynamic programming cutoff grade optimization model is established by the target function of NPV, and ore-body mining sequence, mine production capacity, and ore grade's spatial distribution in different area (optimization unit) were considered, and together combining with the actual mining method. The model achieves the cutoff grade dynamic optimization in underground min both in time and in space. This model makes a significant breakthrough on cutoff grade optimization method in underground mine.
The dissertation also based on the Lane's method theory, I analyze the differences between underground mining and open-pit mining, and then deduce mathematics models of cutoff grade optimization of underground mining of the two phrases in mining and mill and the three phrases in mining, mill and smelting. These models add parameters as depletion rate and wall rock grade, and use the variable of ratio of wall rock grade and ore geological grade. Then it can fit for the underground mine.
Based on the mathematic models of two optimizations method, relevant computer software system is explored, that is, Dynamic Programming Optimize System (DPOS1.0) and Mine Economy Decision-making System (MEDS1.0). DPOS1.0 not only can get each optimization unit's mining quantity, cutoff grade, accumulative production life and NPV, but also can get all the valid decision-makings and the best strategy of the optimization object directly through dynamic programming network diagram.MEDS1.0 not only can consider the whole ore-body as optimization object, but also can consider the arbitrarily selected ore-body scope between reconnoiter line and plane line as optimization object, and it can use many series of technical and economic parameter schemes, so that it can make up the traditional NPV optimization method shortcomings of supposing grade distribution to be unchangeable in optimization scope. Though MEDST1.0 is explored based on the Zambia Chambishi copper mine, it can be applied to other mines, so it is a relatively general mine economy decision-making software.
The cutoff grade dynamic optimize method application on Zambia Chambishi copper mine, and the optimize scope is two mining phases with avalanche mining method. Dynamic programming method divides the optimization scope into 12 optimization units(the phase of dynamic programming) and each optimization unit has its grade distribution according to the defined mining sequence. The optimize result is:cutoff grade and mining quantity from optimization 1 to 12 are respectively:1.004% and 853823.852 ton,0.808% and 1333158.948 ton,0.905% and 913919.33 ton,1.002% and 883214.087 ton,1.015% and 906692.185 ton, 0.999% and 965396.035 ton,0.995% and 716111.732 ton,1.007% and 708986.005 ton, 0.993% and 710850.398 ton,0.993% and 759790.244 ton,0.993% and 709781.188 ton, 0.989% and 740540.653 ton, the total mining quantity is 10202264.66 ton, production life-span is about 10 years, the maximum NPV is 242816.8 thousand US dollars. The cutoff grade optimization is between 0.808% and 1,015%.According to cutoff grade 1% that was used by the mine now, the total mining quantity is 9719937.8 ton, production life-span is about 9 years and 5 months and the maximum NPV is 239817.6 thousand US dollars.
国内外在边界品位研究中经历了50多年的历史,尽管做出了许多非常有价值的成果,但还存在不足：盈亏平衡法得到的边界品位,是一个与矿石质量、时间和位置无关的静态区分标准,没有考虑资金的时间价值,它的不合理性是显而易见的,这种方法逐渐被淘汰；最大现值法是假设整个优化范围的品位服从同一统计学分布,即这一分布在该范围是处处相同。在这个假设条件下,得到使总净现值最大的优化结果是边界品位逐年下降。现实中几乎所有矿床都不满足这一假设条件,矿床一般都有高品位区和低品位区。当低品位区位于矿床的上部时,开始一个时期采用高的边界品位显然是不合理的,甚至是无法实现的。因此,要得到符合实际的最优边界品位,必须考虑矿床不同区段的真实品位分布。
针对边界品位优化研究中存在的问题,在研究地下开采工艺的基础上,根据矿床的赋存条件和矿体的开采顺序,把优化范围划分为一系列的区段,即优化单元。在此基础上,将开采过程分成前后过渡的开采阶段,每个开采阶段包括若干个状态,一个阶段的一个状态由从开始到该阶段开采完毕的累积开采矿量作为状态变量,一个阶段的一个状态对应的开采矿量是从过渡到该状态的前一阶段某状态的累积矿量和本状态的累积矿量求的。开采方案从第一阶段的各状态开始,从优化单元1的品位—矿量曲线上得到各状态矿量对应的边界品位,根据开采过程中发生的投资与使用的采矿方法所发生的生产成本计算出开采矿量所得的赢利,再根据矿山的年生产能力计算出开采时间,并将赢利折现到开采初期时的净现值。这样第一阶段完成后,就得到该阶段各状态的矿量、边界品位和净现值。第二阶段各状态是由第一阶段的某些状态过渡而来。以第二阶段的某个状态为例,假设第一阶段中有k个状态可以过渡到该状态,每个过渡都有一个本阶段开采的矿量,这个矿量是在优化单元2开采的,从第二优化单元的品位—矿量曲线可以得到这一矿量对应的边界品位值、获得的利润以及该利润折现到开采初期时的净现值。该状态的净现值就等于过渡到该状态的前一阶段状态的净现值加上开采矿量获得利润通过折现后的净现值,从前阶段的k个状态过渡到本阶段有k个不同的净现值,该状态的净现值取这k个不同净现值中的最大者,而该状态的边界品位就是获得最大净现值时对应的边界品位。用同样的方法一直计算到最后阶段(最后一个优化单元)每个状态的净现值和边界品位。从最后阶段的各状态中找出净现值最大的状态,按过渡的顺序反推回去,就得到每个阶段的最优过渡(也叫最优决策),这些最优决策组成该边界品位优化问题的最优解。根据上述优化思路,建立了新的动态规划边界品位优化模型。该模型以净现值为指标函数,同时考虑矿体的开采顺序、矿山的年生产能力以及矿石品位在不同区段(优化单元)的实际分布,并与实际使用的采矿方法相结合。该模型实现了地下开采边界品位优化在时间上与空间上的动态结合,在地下开采边界品位优化方法的一次突破。
论文还基于Lane法的思路,分析地下开采和露天开采的不同特点,推导出采矿、选矿两阶段和采矿、选矿、冶炼三阶段的地下开采边界品位优化数学模型。模型增加了贫化率和围岩品位等参数,引用围岩品位与矿石地质品位比值的变量,使之适用于地下矿山。
基于两种优化方法的数学模型,开发了相应的计算机软件系统：动态规划优化系统(DPOS1.0)和矿山经济决策系统(MEDS1.0)。DPOS1.0不仅可以求得各优化单元的开采矿量、边界品位、累计的生产年限以及现值等结果,还可以通过动态规划网络图,直观的得到各优化单元之间有效的决策集合和该优化问题的最优策略。MEDS1.0不仅可以对整个矿体作为优化对象,还可以选取任意勘探线和水平之间的范围作为优化对象,同时能够使用多套经济技术参数方案,弥补了传统现值法假设优化范围品位分布不变的局限性。该系统是基于谦比西铜矿开发的,但也可以应用于其他同类矿山,是一个相对通用的矿山经济决策软件。
这一边界品位动态优化方法应用于赞比亚谦比西铜矿,对崩落法开采的两个阶段的边界品位进行了优化。动态优化法将优化范围划分为12个优化单元(动态规划的阶段),每个优化单元有自己的品位分布,按照一定的开采顺序。优化的结果是：优化单元1到12的边界品位和开采矿量分别是1.004%和853823.852吨、0.808%和1333158.948吨、0.905%和913919.33吨、1.002%和883214.087吨、1.015%和906692.185吨、0.999%和965396.035吨、0.995%和716111.732吨、1.007%和708986.005吨、0.993%和710850.398吨、0.993%和759790.244吨、0.993%和709781.188吨、0.989%和740540.653吨,共开采矿石10202264.66吨,开采时间近10年,最大现值为24281.68万美元,边界品位优化结果在0.808%至1.015%之间。按照目前矿山使用的边界品位1%计算,共开采矿量9719937.8吨,开采时间9年5个月,最大现值为23891.76万美元。
Cutoff grade is one of the most basic and important parameters in mining process. The selection of cutoff grade affects the shape of the enclosed ore-body and ore reserves directly, and then affects mine construction, scale of production, income of mine, facilities selection, and production life-span, and even utilization rate of non-renewable resource. Therefore, cutoff grade is a major impact on the technical and economic parameters both in mine economic benefits and social benefits. Cutoff grade optimization is also one of the core content in mine management parameters' optimization.
Scholars of domestic and foreign had made many valuable achievements about cutoff grade studies in the last 50 years,but it had the following insufficiencies:Cutoff grade which is defined by the profit and loss balance Method,is one static discrimination standard,which has nothing to do with the ore quality, the time and the position,and it don't considere the time value. Inconsequence of this method is obviously, therefore it is eliminated gradually. The Maximum NPV Method supposes that cutoff grade in entire optimization scope obediences identical statistics distribution, that is to say, this distribution is identical everywhere in this scope. Under this hypothesis, optimized result that make the total NPV maximum is that cutoff grade decreased year by year. But in practice, almost all deposits don't meet this hypothetical condition, and they generally have low-grade and high-grade areas. When the low-grade area was located at the upside of the deposit, mining process by a high cutoff grade is obviously unreasonable and even impossible to achieve. In order to obtain the optimal cutoff grade that accords with the actual practice, we must consider the actual grade distribution in the different sections of the deposit.
Aiming at the insufficiencies of the cutoff grade optimization studies, basing on the research of underground mining technology, and according to the mineral deposit conditions and ore mining sequence, the optimization scope was divided into a series of sections, namely optimize units. On this basis, the mining process is divided into transition mining stage of the before and after,and a stage include a number of states.The state variable of a stage was showed by cumulate mining quantity from start to this stage mining finished. Mining quantity of a state in a stage is gained from cumulate mining quantity of the state in this stage and cumulate mining quantity of the transition state of preceding stage.The mining scheme begins from each states of the first stage. Cutoff grade of every state could be obtained from the graph of distribution and grade VS mine quantity of optimize unit-1.Profit of mining quantity could be calculated by the investment of mining process and the cost of mining by the corresponding mining method. Then, according to the annual production capacity of mine, the production life-span could be calculated, and the profit could convert into the NPV of initial stage. After the first stage, mining quantity, cutoff grade and NPV of each state of this stage could be obtained. Every state of the second stage was come from certain state of the first stage. Taking one state of the second stage as an example, supposing that this state could be transited by K states in the first stage and every transition has a mining quantity which is mined in optimize unit-2. So the cutoff grade, the profit and its NPV(discount to initial stage) can be obtained from the graph of distribution and grade VS mine quantity of optimize unit-2. NPV of this state is equal to that NPV of the former transition state add on NPV obtained by the mining quantity. NPV of this state was maximal one among the K-NPVs which come from the K-states of former stage. And the cutoff grade of this state was the one which corresponds with the maximum NPV.The cutoff grade and the NPV of each state were calculated to the final stage (final optimize unit) with similar method. Find out the having maximum NPV of the state in last stage and deduced by reverse sequence of the transition order, then the optimal transition (also called optimal decision-making) of every stage was obtained. The optimal result of this cutoff grade optimization problem was composed of all optimal decision-makings. According to the above optimization ideas, a new dynamic programming cutoff grade optimization model is established by the target function of NPV, and ore-body mining sequence, mine production capacity, and ore grade's spatial distribution in different area (optimization unit) were considered, and together combining with the actual mining method. The model achieves the cutoff grade dynamic optimization in underground min both in time and in space. This model makes a significant breakthrough on cutoff grade optimization method in underground mine.
The dissertation also based on the Lane's method theory, I analyze the differences between underground mining and open-pit mining, and then deduce mathematics models of cutoff grade optimization of underground mining of the two phrases in mining and mill and the three phrases in mining, mill and smelting. These models add parameters as depletion rate and wall rock grade, and use the variable of ratio of wall rock grade and ore geological grade. Then it can fit for the underground mine.
Based on the mathematic models of two optimizations method, relevant computer software system is explored, that is, Dynamic Programming Optimize System (DPOS1.0) and Mine Economy Decision-making System (MEDS1.0). DPOS1.0 not only can get each optimization unit's mining quantity, cutoff grade, accumulative production life and NPV, but also can get all the valid decision-makings and the best strategy of the optimization object directly through dynamic programming network diagram.MEDS1.0 not only can consider the whole ore-body as optimization object, but also can consider the arbitrarily selected ore-body scope between reconnoiter line and plane line as optimization object, and it can use many series of technical and economic parameter schemes, so that it can make up the traditional NPV optimization method shortcomings of supposing grade distribution to be unchangeable in optimization scope. Though MEDST1.0 is explored based on the Zambia Chambishi copper mine, it can be applied to other mines, so it is a relatively general mine economy decision-making software.
The cutoff grade dynamic optimize method application on Zambia Chambishi copper mine, and the optimize scope is two mining phases with avalanche mining method. Dynamic programming method divides the optimization scope into 12 optimization units(the phase of dynamic programming) and each optimization unit has its grade distribution according to the defined mining sequence. The optimize result is:cutoff grade and mining quantity from optimization 1 to 12 are respectively:1.004% and 853823.852 ton,0.808% and 1333158.948 ton,0.905% and 913919.33 ton,1.002% and 883214.087 ton,1.015% and 906692.185 ton, 0.999% and 965396.035 ton,0.995% and 716111.732 ton,1.007% and 708986.005 ton, 0.993% and 710850.398 ton,0.993% and 759790.244 ton,0.993% and 709781.188 ton, 0.989% and 740540.653 ton, the total mining quantity is 10202264.66 ton, production life-span is about 10 years, the maximum NPV is 242816.8 thousand US dollars. The cutoff grade optimization is between 0.808% and 1,015%.According to cutoff grade 1% that was used by the mine now, the total mining quantity is 9719937.8 ton, production life-span is about 9 years and 5 months and the maximum NPV is 239817.6 thousand US dollars.
引文
[1]Montimer G.J.,Grade Control [J],Trans. Inst. Min. and Metal,1950(3),357-399
[2]Musgrove P.,Lead grade-tonnage relation[J],Mining Magazine,1965(112),36-44
[3]Krige D.G, Effective pay limits for selective mining[J],J.S Afr. Inst. Mining Metal,62 Jan.,1962,345-363
[4]Erickson J.D.,Long-time Open Pit Planning[J],Mining Engineering,1968(2), 75-88
[5]Taylor, H.K, General Background Theory of Cutoff Grade[J],Trans. Inst. Min. and Metal,1972(81),160-179
[6]彭兆德、云庆夏等,采矿手册第四卷[M],北京：冶金工业出版社,1991,24-28
[7]陈希廉等,矿业经济学[M],北京：中国国际广播出版社,1992,27-28
[8]郑学敏,矿床工业品位分析与经济品位应用[J],195-2005Tsinghua Tongfang Optical Disc. Co.,Ltd.10-13
[9]胡铁流,市场经济条件下矿产工业指标的变革[J],金属矿山,1998(2),18-20
[10]魏一鸣、童光煦,矿床技术经济评价现状及未来发展[J],黄金,1995(8),10-12
[11]解世俊,矿床地下开采理论与实践[M],北京：冶金工业出版社,1990,27-36
[12]张玉清,矿山技术经济学[M],北京：冶金工业出版社,1987,62-67
[13]Robert D. Cairns,Takayoshi shinkuma,The choice of the cutoff grade in mining[J],Resource policy,2003(29),75-81
[14]解世俊,金属矿床地下开采[M],北京：冶金工业出版社,1986,89-101
[15]王青,史维祥主编,采矿学[M],北京：冶金工业出版社,2001,327,377-387
[16]Taylor, H.K, Mine valuation and Feasibility studies[J],Mineral Industry Cost, Northwest Mining Association,1977(2),1-17
[17]彭兆德、云庆夏等,采矿手册第七卷[M],北京：冶金工业出版社,1991,38-39
[18]谢英亮,露天矿边际品位最优化的经济分析[D],长沙：中南大学,2004
[19]李祥仪、李仲学,矿业经济学[M],北京：冶金工业出版社,2001,89-90
[20]高福德、吴双生等,矿山开发地质经济概论[M],北京：冶金工业出版社,1991,10-15
[21]陈希廉等,矿产经济学[M]，北京：中国广播出版社,1992,27-33
[22]任毅、孙英健,市场价格波动与选别式地下开采边界品位控制[J],有色金属,1998(8),21-27
[23]谢英亮、高阳,论矿产品价格波动与采矿边际品位的调整[J],中国矿业,2003(6),70-72
[24]Taylor, H.K, Cutoff Grades-Some Further Reflections,Trans. Inst. Min. Metal., (Section A,Mining Industry),1985(5),A04-16
[25]李祥仪、李仲学,矿业经济学导论[M],北京：冶金工业出版社,1994,1-23
[26]Henning U.,Calculation of cutoff grade,Can. Mining J.,1963(3),54-57
[27]Lane, K.F., Choosing Cutoff Grade[J],Colorado School of Mines quarterly,1964 (59-4),811-829
[28]Lane, K.F., Commercial Aspects of Choosing Cutoff grade[J],16th APCOM Symposium,1979,280-285.
[29]Lane, K.F.,Economic Definition of Ore----Cutoff grade in Theory and Practice[J],Mining Journal books,London 1988,211-232
[30]Taylor, H.K, The northern porphyries:Local feature and their effects on valuation and planning[J],Mining Engineering,1980(11),41-67
[31]Taylor, H.K,Cutoff grade-some further reflections[J],Trans. Inst. Mining Metallurgy,1985,Vol.94,A204-216
[32]Nilsson D.,Optimum cutoff Grade in Underground Mining,Canada Mining Journal,1982(11),65-70
[33]Arnold R.P. and George V.S.,Planning and Operational cutoff Grades Based om Computerized Net Present Value and Net Cash Flow,CIM Bulletin,1985(1),47-51
[34]Schaap,W.,Principles of an Adaptive Concentrator Cutoff Grade Policy,Trans. Inst. Min. Metal,(Section A,Mining Industry),1986(1),A15-21
[35]Blackwell, M.R.L Some Aspects of the Evaluation and Planning of the Bougainville Copper Project[J],Decision Making in Mineral Industry,1970(12), 261-269
[36]Koniaris,E.A,Positive Approach to Long Term Mine Planning in Open Pit Mine[D],PH.D thesis, Mining Dept. Queen's University,Kingston.1991
[37]Robert D.Cairns,Takayoshi Shinkuma,The Choice of Cutoff Grade in Mining[J],Resource Policy[J],2003(29),75-81
[38]Takayoshi Shinkuma,Takashi Nishiyama,The Grade Selection Rule of the Metal Mines,an Empirical Study on Copper Mines[J],Resource Policy,2000(26),31-38
[39]M.Ataei、M.Osanloo,Methods for Calculation of Optimal Cutoff Grade in Complex Ore Deposits[J],Journal of Mining Science,2003(39-5),499-507
[40]H.Wagner,How to Address the Crisis of Mining Engineering Education in the Western World[J],Mineral Resource Engineering,1999(8),471-481
[41]H.Wagner, G.B.L.Fettweis,About Science and Technology in the Field of Mining in the Western World at the Beginning of the New Century[J],Resource Policy,2001 (27),157-168
[42]王青,史维祥主编,采矿学[M],冶金工业出版社,2001,377-386
[43]郑学敏,矿床工业品位分析与经济品位应用[J],1994-2006China Academic Journal Electric Publishing House。Http://www.cnki.net,10-13
[44]仲崇波、金镜潭,黄金矿山盈亏平衡品位分析的探讨[J],沈阳黄金学院学报,1995(3),67-70
[45]苑香民、王会文等,黄金矿山采矿规模设计的不确定性分析[J],黄金,2002(12),18-21
[46]李德斌,利用盈亏平衡品位进行黑斑矿的采选决策[J],有色金属,2003(11),173-176
[47]向鹏成,应用盈亏平衡分析法确定低品位矿利用的临界品位[J],冶金矿山设计与建设,2001(11),24-27
[48]王青、王之静,露天开采整体优化------理论模型和算法[M]。北京：冶金工业出版社,2000,56-60
[49]Roman R.J.,The Use of Dynamic Programming for Determining Mine-mill Production Schedules[J],Application of computer methods in the Mineral Industry(Johannesburg:South African IMM 1973,65-70
[50]Jorgen Elbrond etc.,Use of an Interactive Dynamic Programming System as an Aid to Mine Evaluation[J],Proceeding,17th Apcom,463-474
[51]Yves Lizotte、Jorgen Elbrond,Choice of Mine-mill Capacities and Production Schedules Using Open-ended Dynamic Programming[J],CIM Bulletin,1982(3), 154-163
[52]Dowd P.A.,The Use of Dynamic Programming in Cutoff Grade Determination [J],Tech. Rep. Dep. Genie Miner,1975(4),11-29
[53]Dowd P.A.,Application of Dynamic and Stochastic Programming to Optimize Cutoff Grades and Production rates[J],Trans. Inst. Mining,1976(1),Sect. A, Vol.85, A22-A31
[54]Noren N.E.,Long-Range Decision Models in Mining[J],Economic Research Institute,1969(12),240-253
[55]N.M. Satybaldievv和A.M. Freidin,Optimization of mineral mining geometry and mine production capacity[J],Journal of Mining Science,Vol.42,2006(5),27-34
[56]Qing Wang,Long-term Open-pit Production Scheduling Through Dynamic Phrase-bench Scheduling[J],Trans. Inst. Min. Metall.(Section A:Mine Industry), 105,May-August,1996,A99-103
[57]李泽临,边界品位小议[J],有的金属,1981(6),39-40
[58]王惠民,浅谈矿石工业指标[J],化工矿山技术,1982(3),47-50
[59]任启明,确定矿山工业指标中几个问题的探讨[J],冶金经济分析,1983(4),36-41
[60]王介甫,许楚彬,关于矿床工业指标的研究[J],化工矿山技术,1984(6),9-14
[61]侯景儒,黄竞先等,对数正态克立格法的理论及应用[J],北京科技大学学报,1998(11),391-398
[62]侯景儒,潘汉军等,多元地质统计学的基本理论与方法[J],北京科技大学学报,1992(14),95.103
[63]侯景儒,王志民等,湖南桃江锰矿地质统计学及数学地质研究[J],中国南方锰矿地质,1992(33),34-40
[64]徐熹,矿石级差品位指标体系与兰纳的边界品位理论[J],数量经济技术经济研究,1985(14),41-47
[65]任毅,市场经济下金属露天矿边界品位的优化与控制[J],金属矿山,1997(2),1-6
[66]任毅,露天矿次边界品位和次品位堆储的优化决策[J],有色金属,1997(3),10-17
[67]黄光球,露天开采矿体边界品位动态优化新方法[J],中国锰业,1995(5),18-22
[68]黄光球,地下开采矿体边界品位动态优化法[J],化工矿山技术,1997(4),1-6
[69]谢英亮,基于控制论的露天矿边际品位最优化[J],金属矿山,2000(11)14-16
[70]谢英亮,基于期权定价的矿业投资决策[J],冶金矿山设计与建设,2001(4),22-25
[71]谢英亮,露天矿边际品位优化及其动态调整模型[J],金属矿山,1996(7),11-17
[72]谢英亮,半投入产出模型及求解[J],系统工程理论与实践,1996(7),7-11
[73]黄光球,露天矿边界品位的动态最优化及人工神经网络的应用[J],中国矿业,1996(4),32-38
[74]赵德孝，柳小波等,金山店铁矿入选品位动态优化数学模型建立[J],金属矿山,2004(4),8-10
[75]姜谙男,赵德孝等,矿石入选品位优化决策支持系统的开发[J],矿业研究与开发,2003(4),43-45
[76]云庆夏,矿石品位优化的遗传算法[J],金属矿山,1997(5),13-16
[77]李克庆,刘保顺,确定合理入选品位的通用系统[J],北京科技大学学报,1997(10),28-31
[78]长沙黑色矿山设计研究院,黑色冶金矿山技术经济设计参考资料(自编)[M],1979,82-93
[79]王成发,关于经济地质学的几个问题[J],矿产地质动态,1984(3),6-9
[80]王真民,用动态观点研究生产矿山品位指标的探讨[J],中国钼业,1998(22),14-19
[81]王兵,我矿最低工业品位和边界品位确定方法的探讨[J],新疆有色金属,2001(1),8-12
[82]徐玖平等,运筹学[M],北京：科学出版社,2004,119-125
[83]熊义杰,运筹学教程[M],北京,国防工业出版社,2004,126-135
[84]刘建永等,运筹学算法与编程实践----Delphi实现[M],北京：清华大学出版社,2004,214-249
[85]刘光中,动态规划理论及其应用[M],成都：成都科技大学出版社,
[86]初道忠,王青,任凤玉,国外某地下铜矿边界品位的研究[J],中国矿业,2007,(4),94-97
[87]初道忠,王青,丁一,刘建兴,地下开采矿体边界品位的确定方法[J],矿冶工程,2007,(4),6-91990,20-101
[88]高校财经数据库http://www.bjinfobank.com
[89]王勇领,系统分析与设计[M],北京：清华大学出版社,1991
[90]蔡淑琴,管理信息系统[M],北京：科学出版社,2004
[91]常柏林,概率与数理统计[M],北京：高等教育出版社,1993
[92](美)BRIAN OVERLAND,董梁,李君龙,李自更等译。C++语言命令详解(第二版)[M],北京：电子工业出版社,2000
[93]夏云龙,最新Visual C++使用手册[M],北京：电子工业出版社,2005
[94]王瑞等,Visual C++使用手册[M],北京人民邮电出版社,2006
[95]帕特里克、高京义等,SQL基础[M],北京：清华大学出版社,2003
[96]杨志姝等,SQL应用与开发标准教程[M],北京：清华大学出版社,2006
[97]郑小玲,ACCESS 2003中文版[M],北京：清华大学出版社,2004。
[98]张世雄等,矿物资源开发工程[M],武汉：武汉工业大学出版社,2000,113-116
[99]初道忠,王青,李广军,矿山经济决策系统的开发,金属矿山,2007,(3),18-20
[100]张世雄等,矿物资源开发工程[M],武汉：武汉工业大学出版社,2000,113-116
[101]袁雨怀、舒航,矿产经济理论与实践[M],北京：冶金工业出版社,1993,42-67
[2]Musgrove P.,Lead grade-tonnage relation[J],Mining Magazine,1965(112),36-44
[3]Krige D.G, Effective pay limits for selective mining[J],J.S Afr. Inst. Mining Metal,62 Jan.,1962,345-363
[4]Erickson J.D.,Long-time Open Pit Planning[J],Mining Engineering,1968(2), 75-88
[5]Taylor, H.K, General Background Theory of Cutoff Grade[J],Trans. Inst. Min. and Metal,1972(81),160-179
[6]彭兆德、云庆夏等,采矿手册第四卷[M],北京：冶金工业出版社,1991,24-28
[7]陈希廉等,矿业经济学[M],北京：中国国际广播出版社,1992,27-28
[8]郑学敏,矿床工业品位分析与经济品位应用[J],195-2005Tsinghua Tongfang Optical Disc. Co.,Ltd.10-13
[9]胡铁流,市场经济条件下矿产工业指标的变革[J],金属矿山,1998(2),18-20
[10]魏一鸣、童光煦,矿床技术经济评价现状及未来发展[J],黄金,1995(8),10-12
[11]解世俊,矿床地下开采理论与实践[M],北京：冶金工业出版社,1990,27-36
[12]张玉清,矿山技术经济学[M],北京：冶金工业出版社,1987,62-67
[13]Robert D. Cairns,Takayoshi shinkuma,The choice of the cutoff grade in mining[J],Resource policy,2003(29),75-81
[14]解世俊,金属矿床地下开采[M],北京：冶金工业出版社,1986,89-101
[15]王青,史维祥主编,采矿学[M],北京：冶金工业出版社,2001,327,377-387
[16]Taylor, H.K, Mine valuation and Feasibility studies[J],Mineral Industry Cost, Northwest Mining Association,1977(2),1-17
[17]彭兆德、云庆夏等,采矿手册第七卷[M],北京：冶金工业出版社,1991,38-39
[18]谢英亮,露天矿边际品位最优化的经济分析[D],长沙：中南大学,2004
[19]李祥仪、李仲学,矿业经济学[M],北京：冶金工业出版社,2001,89-90
[20]高福德、吴双生等,矿山开发地质经济概论[M],北京：冶金工业出版社,1991,10-15
[21]陈希廉等,矿产经济学[M]，北京：中国广播出版社,1992,27-33
[22]任毅、孙英健,市场价格波动与选别式地下开采边界品位控制[J],有色金属,1998(8),21-27
[23]谢英亮、高阳,论矿产品价格波动与采矿边际品位的调整[J],中国矿业,2003(6),70-72
[24]Taylor, H.K, Cutoff Grades-Some Further Reflections,Trans. Inst. Min. Metal., (Section A,Mining Industry),1985(5),A04-16
[25]李祥仪、李仲学,矿业经济学导论[M],北京：冶金工业出版社,1994,1-23
[26]Henning U.,Calculation of cutoff grade,Can. Mining J.,1963(3),54-57
[27]Lane, K.F., Choosing Cutoff Grade[J],Colorado School of Mines quarterly,1964 (59-4),811-829
[28]Lane, K.F., Commercial Aspects of Choosing Cutoff grade[J],16th APCOM Symposium,1979,280-285.
[29]Lane, K.F.,Economic Definition of Ore----Cutoff grade in Theory and Practice[J],Mining Journal books,London 1988,211-232
[30]Taylor, H.K, The northern porphyries:Local feature and their effects on valuation and planning[J],Mining Engineering,1980(11),41-67
[31]Taylor, H.K,Cutoff grade-some further reflections[J],Trans. Inst. Mining Metallurgy,1985,Vol.94,A204-216
[32]Nilsson D.,Optimum cutoff Grade in Underground Mining,Canada Mining Journal,1982(11),65-70
[33]Arnold R.P. and George V.S.,Planning and Operational cutoff Grades Based om Computerized Net Present Value and Net Cash Flow,CIM Bulletin,1985(1),47-51
[34]Schaap,W.,Principles of an Adaptive Concentrator Cutoff Grade Policy,Trans. Inst. Min. Metal,(Section A,Mining Industry),1986(1),A15-21
[35]Blackwell, M.R.L Some Aspects of the Evaluation and Planning of the Bougainville Copper Project[J],Decision Making in Mineral Industry,1970(12), 261-269
[36]Koniaris,E.A,Positive Approach to Long Term Mine Planning in Open Pit Mine[D],PH.D thesis, Mining Dept. Queen's University,Kingston.1991
[37]Robert D.Cairns,Takayoshi Shinkuma,The Choice of Cutoff Grade in Mining[J],Resource Policy[J],2003(29),75-81
[38]Takayoshi Shinkuma,Takashi Nishiyama,The Grade Selection Rule of the Metal Mines,an Empirical Study on Copper Mines[J],Resource Policy,2000(26),31-38
[39]M.Ataei、M.Osanloo,Methods for Calculation of Optimal Cutoff Grade in Complex Ore Deposits[J],Journal of Mining Science,2003(39-5),499-507
[40]H.Wagner,How to Address the Crisis of Mining Engineering Education in the Western World[J],Mineral Resource Engineering,1999(8),471-481
[41]H.Wagner, G.B.L.Fettweis,About Science and Technology in the Field of Mining in the Western World at the Beginning of the New Century[J],Resource Policy,2001 (27),157-168
[42]王青,史维祥主编,采矿学[M],冶金工业出版社,2001,377-386
[43]郑学敏,矿床工业品位分析与经济品位应用[J],1994-2006China Academic Journal Electric Publishing House。Http://www.cnki.net,10-13
[44]仲崇波、金镜潭,黄金矿山盈亏平衡品位分析的探讨[J],沈阳黄金学院学报,1995(3),67-70
[45]苑香民、王会文等,黄金矿山采矿规模设计的不确定性分析[J],黄金,2002(12),18-21
[46]李德斌,利用盈亏平衡品位进行黑斑矿的采选决策[J],有色金属,2003(11),173-176
[47]向鹏成,应用盈亏平衡分析法确定低品位矿利用的临界品位[J],冶金矿山设计与建设,2001(11),24-27
[48]王青、王之静,露天开采整体优化------理论模型和算法[M]。北京：冶金工业出版社,2000,56-60
[49]Roman R.J.,The Use of Dynamic Programming for Determining Mine-mill Production Schedules[J],Application of computer methods in the Mineral Industry(Johannesburg:South African IMM 1973,65-70
[50]Jorgen Elbrond etc.,Use of an Interactive Dynamic Programming System as an Aid to Mine Evaluation[J],Proceeding,17th Apcom,463-474
[51]Yves Lizotte、Jorgen Elbrond,Choice of Mine-mill Capacities and Production Schedules Using Open-ended Dynamic Programming[J],CIM Bulletin,1982(3), 154-163
[52]Dowd P.A.,The Use of Dynamic Programming in Cutoff Grade Determination [J],Tech. Rep. Dep. Genie Miner,1975(4),11-29
[53]Dowd P.A.,Application of Dynamic and Stochastic Programming to Optimize Cutoff Grades and Production rates[J],Trans. Inst. Mining,1976(1),Sect. A, Vol.85, A22-A31
[54]Noren N.E.,Long-Range Decision Models in Mining[J],Economic Research Institute,1969(12),240-253
[55]N.M. Satybaldievv和A.M. Freidin,Optimization of mineral mining geometry and mine production capacity[J],Journal of Mining Science,Vol.42,2006(5),27-34
[56]Qing Wang,Long-term Open-pit Production Scheduling Through Dynamic Phrase-bench Scheduling[J],Trans. Inst. Min. Metall.(Section A:Mine Industry), 105,May-August,1996,A99-103
[57]李泽临,边界品位小议[J],有的金属,1981(6),39-40
[58]王惠民,浅谈矿石工业指标[J],化工矿山技术,1982(3),47-50
[59]任启明,确定矿山工业指标中几个问题的探讨[J],冶金经济分析,1983(4),36-41
[60]王介甫,许楚彬,关于矿床工业指标的研究[J],化工矿山技术,1984(6),9-14
[61]侯景儒,黄竞先等,对数正态克立格法的理论及应用[J],北京科技大学学报,1998(11),391-398
[62]侯景儒,潘汉军等,多元地质统计学的基本理论与方法[J],北京科技大学学报,1992(14),95.103
[63]侯景儒,王志民等,湖南桃江锰矿地质统计学及数学地质研究[J],中国南方锰矿地质,1992(33),34-40
[64]徐熹,矿石级差品位指标体系与兰纳的边界品位理论[J],数量经济技术经济研究,1985(14),41-47
[65]任毅,市场经济下金属露天矿边界品位的优化与控制[J],金属矿山,1997(2),1-6
[66]任毅,露天矿次边界品位和次品位堆储的优化决策[J],有色金属,1997(3),10-17
[67]黄光球,露天开采矿体边界品位动态优化新方法[J],中国锰业,1995(5),18-22
[68]黄光球,地下开采矿体边界品位动态优化法[J],化工矿山技术,1997(4),1-6
[69]谢英亮,基于控制论的露天矿边际品位最优化[J],金属矿山,2000(11)14-16
[70]谢英亮,基于期权定价的矿业投资决策[J],冶金矿山设计与建设,2001(4),22-25
[71]谢英亮,露天矿边际品位优化及其动态调整模型[J],金属矿山,1996(7),11-17
[72]谢英亮,半投入产出模型及求解[J],系统工程理论与实践,1996(7),7-11
[73]黄光球,露天矿边界品位的动态最优化及人工神经网络的应用[J],中国矿业,1996(4),32-38
[74]赵德孝，柳小波等,金山店铁矿入选品位动态优化数学模型建立[J],金属矿山,2004(4),8-10
[75]姜谙男,赵德孝等,矿石入选品位优化决策支持系统的开发[J],矿业研究与开发,2003(4),43-45
[76]云庆夏,矿石品位优化的遗传算法[J],金属矿山,1997(5),13-16
[77]李克庆,刘保顺,确定合理入选品位的通用系统[J],北京科技大学学报,1997(10),28-31
[78]长沙黑色矿山设计研究院,黑色冶金矿山技术经济设计参考资料(自编)[M],1979,82-93
[79]王成发,关于经济地质学的几个问题[J],矿产地质动态,1984(3),6-9
[80]王真民,用动态观点研究生产矿山品位指标的探讨[J],中国钼业,1998(22),14-19
[81]王兵,我矿最低工业品位和边界品位确定方法的探讨[J],新疆有色金属,2001(1),8-12
[82]徐玖平等,运筹学[M],北京：科学出版社,2004,119-125
[83]熊义杰,运筹学教程[M],北京,国防工业出版社,2004,126-135
[84]刘建永等,运筹学算法与编程实践----Delphi实现[M],北京：清华大学出版社,2004,214-249
[85]刘光中,动态规划理论及其应用[M],成都：成都科技大学出版社,
[86]初道忠,王青,任凤玉,国外某地下铜矿边界品位的研究[J],中国矿业,2007,(4),94-97
[87]初道忠,王青,丁一,刘建兴,地下开采矿体边界品位的确定方法[J],矿冶工程,2007,(4),6-91990,20-101
[88]高校财经数据库http://www.bjinfobank.com
[89]王勇领,系统分析与设计[M],北京：清华大学出版社,1991
[90]蔡淑琴,管理信息系统[M],北京：科学出版社,2004
[91]常柏林,概率与数理统计[M],北京：高等教育出版社,1993
[92](美)BRIAN OVERLAND,董梁,李君龙,李自更等译。C++语言命令详解(第二版)[M],北京：电子工业出版社,2000
[93]夏云龙,最新Visual C++使用手册[M],北京：电子工业出版社,2005
[94]王瑞等,Visual C++使用手册[M],北京人民邮电出版社,2006
[95]帕特里克、高京义等,SQL基础[M],北京：清华大学出版社,2003
[96]杨志姝等,SQL应用与开发标准教程[M],北京：清华大学出版社,2006
[97]郑小玲,ACCESS 2003中文版[M],北京：清华大学出版社,2004。
[98]张世雄等,矿物资源开发工程[M],武汉：武汉工业大学出版社,2000,113-116
[99]初道忠,王青,李广军,矿山经济决策系统的开发,金属矿山,2007,(3),18-20
[100]张世雄等,矿物资源开发工程[M],武汉：武汉工业大学出版社,2000,113-116
[101]袁雨怀、舒航,矿产经济理论与实践[M],北京：冶金工业出版社,1993,42-67