基于稳定价格预期的露天矿山边际品位优化方法

边际品位作为露天矿山开采的核心参数,其合理的选取可以提升资源利用率,增加矿山企业效益.为了实现露天矿山净现值最大化,在金属价格临时变化时对边际品位进行及时调整,提出了一种基于稳定价格预期的露天矿山边际品位优化方法.以某斑岩型露天铜矿为例,基于边际品位的迭代算法,获得稳定价格预期下的最优边际品位策略.拟合露天矿山剩余净现值与剩余矿岩总量的函数关系,再次通过迭代算法获得金属价格临时变动时的机会成本,方便对边际品位进行重新计算.结果表明,稳定价格预期下,矿山最优边际品位在整个生产周期内呈缓慢下降趋势.与采用固定边界品位相比,采用动态边际品位可以获得最大的净现值,并且低品位资源利用价值更大.     

安徽某矿山边界品位动态优化研究

基于盈亏平衡法的思路,推导出边界品位动态优化数学模型.该模型可以根据市场价格的变动,动态确定最低工业品位.这一动态优化方法以安徽某铜矿山为研究对象,先根据当前市场价格,得到最低工业品位,然后在品位区间0.1％～0.4％间按0.05％间距计算各品位矿体储量,采用贴现现金流法对矿山价值进行详细估算,估算结果验证了优化模型的临界值,并以最大累计净现值为指标确定最优开采边界品位.     

某露天铜矿全境界开采规划优化

基于数字矿床模型中的块体模型,在给定的境界内,利用锥体排除法产生一系列地质最优开采体,建立动态规划模型,以净现值最大为目标函数,应用动态规划法对最优开采体进行动态排序,就可以找到最优开采路径作为最优开采方案。将上述方法应用于某露天矿,得出矿区的最佳开采年限为15 a,并给出了每年的开采区域、采矿量、剥岩量以及年末的累积净现值。     

露天开采时矿体边界品位动态优化的神经网络方法

本文提出了以净现值最大为优化目标，考虑采、选、冶生产能力，品位分布以及开采计划要求的露天矿矿体边界品位动态代化模型，并应用神经网络理论提出了该模型的求解方法。     

露天煤矿开采计划的整体动态优化

针对新建或扩建露天煤矿,给出了一个能够同时求得最佳生产能力、采剥顺序和生产寿命的动态优化方法.该方法首先对所研究的矿床建立煤层数字模型,基于这一模型,在最终境界内产生一个“地质最优开采体”序列,然后把序列中的开采体作为状态建立动态规划排序模型,对所有可行的子序列进行经济评价,得出总净现值最大的子序列,这一最佳子序列同时给出了每年的煤炭开采量和剥离量、采剥推进位置与生产寿命.     

边界品位的动态规划优化模型及算法

在分析边界品位优化现有方法存在问题的基础上,提出边界品位动态规划优化模型以及算法步骤。该模型考虑矿体的开采顺序和矿床不同区段的品位分布,实现了地下开采边界品位在时间和空间上的动态结合。基于建立的数学模型,开发了相应的计算机应用系统,并在非洲某铜矿进行了应用。     

露天矿综合配矿模型

以鞍千矿业公司3个采场为例,在分析矿山各采区品位分布信息的基础上,建立了基于0-1整数规划算法的露天矿多采区协同开采资源配置优化的数学模型,并利用C++语言编写了0-1整数规划算法程序,对该模型进行了解算。研究表明:通过进行合理配矿,确保稳定的矿石输出品位,从而保持选矿厂矿石入选品位稳定,实现了提高生产效率、降低生产成本、提高矿产资源利用率的目的。     

边际品位的随机规划优化方法

边际品位的确定必须考虑边际品位在时间、空间上的动态特征以及边际品位分布的随机性。运用随机规划的原理和方法,以净现值为指标函数,结合矿山企业使用的采矿方法,在进行边际品位优化的时候将边际品位在时间上、空间上的动态特征以及边际品位在不同块区分布的随机性作为优化模型的考虑因素,因此得到的最优边际品位最能反映矿山企业的生产真实情况。     

沙溪铜矿开采边界品位动态优化方法

边界品位对矿山而言是一个尤其重要的决策参数。我国的边界品位指标制定于计划经济时期,随着我国市场经济的不断完善,现行的矿产工业指标越来越不能适应采矿工业的发展。沙溪铜矿具有埋藏深、储量大、品位低等特点,如何实现经济合理开采,其中首要解决的便是边界品位的问题。鉴于此,提出以铜品位0.1%为边界圈定矿化域、进行地质统计学估值得到矿化域模型,从而得到矿石储量、平均品位与边界品位的关系的方法,随后提出以最大净现值为目标的边界品位动态优化数学模型和算法。最后,应用所提方法优化了沙溪铜矿边界品位,与原初步设计结果相比,使得矿山服务年限、回收金属量、总现金流量、总净现值都得到了显著提高。该方法对我国大量的储量大、品位低的地下矿床经济开采具有借鉴意义。     

复杂多金属露天矿山最终境界动态综合优化

为了将矿岩时间属性准确加入到复杂多金属露采矿山境界优化过程中, 提出了基于矿床块体模型的动态综合优化方法。采用当量品位的方式将多金属元素转化为综合当量品位并对矿床块模型进行经济参数赋值, 运用L-G图论法通过矿石售价折扣的方式获得一系列静态方案, 研究分析了复杂矿山的开采工艺并对各方案编排进度计划, 统计计算各方案年现金流, 经贴现获得净现值(NPV), 综合分析各方案NPV及资源回收情况确定最优方案, 实现复杂多金属露天矿山最终境界的动态综合优化圈定。基于生产进度计划的境界动态优化方法与矿山实际生产紧密结合, 其优化结果可为矿山设计及未来生产提供更好的基础支撑, 为露采矿山最优境界寻找开辟了一条新的途径。     

基于Whittle的露天境界动态优化研究

开采境界圈定是露天矿山开采设计的基础，境界优化结果的优劣直接制约着矿山的整体发展效益。露天开采过程中面对的是复杂多变的地质岩体、无序的品位分布、多变的经济参数等一系列非线性动态问题，现有的主流境界优化方法未能有效考虑该类问题。为实现对露天矿山境界优化的经济动态评估以及矿山剥采均衡，将露天境界优化与地质品位、矿体赋存状态相结合，根据地质数据库采用SURPAC软件建立了矿体三维实体模型和块段品位模型。借助境界动态优化分析软件Whittle，并根据某矿山实际情况，将浮动圆锥法和LG图论法相结合，在一定的技术、经济指标条件下，生成了一系列不同价格对应的露天境界优化方案。根据矿山设计生产规模，对各个境界方案进行进度计划排产，同时考虑了资金的时间价值，引入贴现率指标，获得了各个方案的最大净现值，确定净现值最大的方案为最优方案。研究表明：该方案的提出，实现了动态条件下该矿山露天境界的高效动态优化，为露天矿山开采境界优化提供了新思路。     

Optimal extraction sequence modeling for open pit mining operation considering the dynamic cutoff grade

The cutoff grade problem is an important research challenge and vital optimization task in the yearly operational planning of open pit mines due to its combinatorial nature. Because of it's influenced by the economic parameters, the capacities of stages in the mining operation, mining sequence, and grade distribution of the deposit. Essentially, it asserts that the dynamic cutoff grade at any given period is a function of the ore availability and the needs of the mill at that period. Consequently, cutoff grades strategy and extraction sequence should be considered, simultaneously. Due to its goal, various attempts have been made to develop a computerized procedure for the extraction sequence of open pit mine. None of the resulting approaches appear to enjoy wide acceptance because of it's the numerous associated variables. A new model is proposed to overcome this shortcoming. This model solves the problem in the three steps: 1) the actual economic loss associated with each type of processing for each block, 2) the probabilities distribution and average grade for each type processing is computed from independent realization, and 3) each block with its expected economic loss is developed as a binary integer programming model. Using this model, the optimum extraction sequences in each period are identified based on the optimum processing decisions. A case study is presented to illustrate the applicability of the model developed. Results showed that the extraction sequences obtained using the suggested model will be realistic and practical. This model allows for the solution of very large problem in reasonable time with very high solution quality in terms of optimal net present value.     

Mixed integer linear programming formulations for open pit production scheduling

One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.     

基于经济时间序列预测的露天矿开采境界动态优化

为获得更为优越的露天矿山境界,构建了集经济时间序列预测、矿岩时间属性赋值和动态经济指标计算为一体的境界全动态优化方法。金属价格是矿山境界优化过程中最重要的因素之一,以金属价格历史数据为平台,通过创建合适时间序列模型,对未来价格做出预测,以预测结果为基础,运用L-G图论法生成系列境界方案,根据矿山实际情况编排进度计划,实现矿岩块参数赋值,将预测结果代入到矿岩块体模型中,计算境界净现值（NPV）,经多方案比较确定最优境界。以某铜矿山为例,通过对近50 a伦敦金属交易所（LME）铜精矿季度平均结算价格分析处理,建立了自回归求和移动平均模型（ARIMA）,实现了未来15 a铜价预测,最终确定了矿山经济最优境界。建立于金属价格预测基础上的境界动态优化方法所得方案NPV更接近生产实际,其优化结果可更好为矿山设计及未来生产提供基础支撑。     

曼家寨锡锌多金属矿床数学经济模型的应用

在建立马关都龙曼家寨锡锌多金属矿床数学经济模型的基础上,依据不同边界品位多方案圈定矿体,并根据所计算出的净现值进行矿床经济评价研究,确定出矿床锌的最佳边界品位为3.2%,实现了矿山企业生产的动态管理和生产方案的优化决策与多目标规划;当锌的边界品位为0.97%时,在曼家寨锡锌多金属矿床开发的经济分析中,产品价格最为敏感,其次为产品成本,再次为投资总额,最为不敏感的是回收服务年限。     

Integrated mine and tailings planning: a mixed integer linear programming model

Long-term mine planning models maximise the net present value of the extracted ore over the mine lifetime. In oil sands mining, further processing of ore material results in massive volumes of tailings slurry. Composite tailings (CT) production is one of the common technologies used for tailings dewatering. In this paper, a tailings model is developed to calculate the volume of CT. An integrated mixed integer linear programming model is developed to optimise the long-term mine planning model with respect to CT production and deposition. The model is verified by carrying out a case study on an oil sands data-set, resulting in integer solution within 1% optimality gap.     

A robust mixed integer linear programming framework for underground cut-and-fill mining production scheduling

ABSTRACT

A review of general optimization studies that have been proposed for underground mining shows that previous works lack flexibility, operability and practicality in relation to cut-and-fill mining production scheduling. This paper presents a robust mixed integer linear programming (MILP) formulation for underground cut-and-fill mining. The objective function of the model is to maximize the net present value (NPV) of the operation while meeting all mining and processing operational and technical constraints. The MILP model features stope development and extraction sequencing constraints, mining and processing tonnage fluctuation constraints, and extraction duration and active levels control constraints. These features make the model more practical and expandable. The MILP model is verified and validated with two case studies from an existing mine and the results are compared with the actual mining strategy. The comparison shows a 9% to 17% improved NPV in both case studies resulting from mining higher grades and processing less tonnes thereby generating a better cash flow.     

基于多目标0-1规划的采掘作业计划优化

为了满足矿山精细化管理的要求,实现生产的安全性和高效性目标,针对地下金属矿山传统计划编制时存在主观性强、实时性差、效率低、误差大以及难以求得全局最优解的弊端,以采掘车间月出矿量、月出矿平均品位、月生产利润为目标,以采场地质条件、车间生产能力、生产任务以及生产原则为约束,构建基于多目标0-1规划的采掘车间作业计划优化模型。模型采用理想点法对目标函数进行降维,决策变量为二维0-1变量,从空间和时间2个维度描述了采掘车间的生产决策状态,简化了模型的求解过程,在LINGO求解器中编写模型语言进行求解,进而得到计划周期内的最优排产方案。以某地下黄金矿山车间作业计划编制为应用案例,解算出某月采场开采的最优时序方案,并用甘特图进行直观展示。结果表明:该模型适用于地下金属矿山采掘作业计划编制,克服了手工编制方法的弊端,保证了采掘车间生产指标的动态平衡,有利于提高矿山的经济效益。     

露天矿配矿优化方法研究

针对露天矿山规划与矿石质量管理的配矿需求, 在爆堆品位分布预测的基础上, 利用0-1整数规划模型, 研究了露天矿配矿的优化方法, 进而将其嵌入到DIMINE软件中, 并以某水泥灰岩矿配矿设计为例, 验证该技术的性能。结果表明, 该露天矿配矿优化方法应用简单、配矿效率高、效果好, 可有效提高企业的经济效益, 对于指导矿山企业的有效生产与决策具有重要的意义。     

Long Term Production Scheduling Optimisation for a Surface Mining Operation: An Application of MineMax™ Scheduling Software

Since long term production scheduling deals with movement of ore and waste during the life of a mine, it has a significant effect on the cash flow of a mining operation. Therefore, mine planners often seek to optimise the production schedule with respect to a given criterion. The most commonly used criterion in long term scheduling optimisation is to maximise net present value (NPV). The process involves sequencing of ore blocks or parcels to be mined in each period over the life of the mine subject to precedence and other physical constraints imposed by the mining system. The complexity of mine production scheduling in practice entails a computer solution using mathematical programming as the optimisation technique. Linear and mixed integer programming techniques have been used to optimise long term production schedules but most of the computer programs based on these make overly simplifying assumptions and lack the flexibility to handle practical considerations of mine scheduling. MineMax? scheduling software is applied to long term scheduling for a multielement surface mining operation. MineMax uses mixed integer programming with the branch and bound algorithm as solution strategy. The system allows the planner to generate a mine production schedule in the same manner as manual scheduling, but making use of the interactivity in planning data input, in-built optimisation algorithm and the speed of the personal computer. This study involves investigation into the effects of reblocking and grade intervals on the mining schedule, specifically, the material movement, milling grade and the cash flow over the life of the mine.