Methods for Calculation of Optimal Cutoff Grades in Complex Ore Deposits

The cutoff grade of valuable components delimits the complex ore reserves suitable for efficient mining. The cutoff grade optimization is conducted to maximize the net present value of products in mining projects. The investigations were realized by using the equivalent grade method, iterated grid search method, genetic algorithm, and golden section search. The software presented ensures the calculation of the optimal production with melting considered and the cutoff grades over the life of mine.     

Cutoff grade optimization algorithm with stockpiling option for open pit mining operations of two economic minerals

Lane's theory of cutoff grade optimization maximizes the Net Present Value (NPV) of an open pit mining operation with a declining effect as the deposit moves toward exhaustion. This declining effect of NPV defines dynamic cutoff grades, i.e. higher cutoff grades in the early years of mine life and lower cutoff grades in the later years. This phenomenon allows the creation of stockpiles with material between the lowest (breakeven) and optimum cutoff grades for processing during later years, when it becomes economical. As an extension to Lane's original theory of cutoff grades in deposits of two economic minerals, the management, i.e. supplies of material from the mine to the stockpile and from the stockpile to the processing plant, is addressed through the development of a cutoff grade optimization algorithm with option to stockpile. The benefits of the methodology are elaborated in a hypothetical case study.     

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.     

矿用物资装载问题的遗传算法研究

为了更好地增强矿山企业内部市场化管理水平,提高矿用物资的仓储、运输等效率,优化装载方案是一项非常重要的技术环节。在对矿用零散货物配装问题分析的基础上,以物资配送的经济效益最大化为目标,兼顾车辆的有效容积和承载量等方面的约束条件,建立了基于优化方法求解的数学模型,并引入模拟生物进化的遗传算法进行了实例研究。应用结果表明,遗传算法在求解矿用物资装载最优方案的过程中,具有收敛速度快、用时短等优点,且计算精度较高;遗传算法良好的适应性和强大的搜索性能,非常适合用于求解多条件约束问题。研究结果有助于矿用零散物资运配送效能的提升,从而促进矿山企业相关物资管理部门经营效益的进一步提高。     

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.     

Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits

One of the most important aspects of mine design is to determine the optimum cut-off grades. Material grading above and below the cut-off is directed to different destinations. Optimization of cut-off grade is now an accepted principle for open pit planning studies. The most commonly criteria used in cut-off grade optimization is to maximize net present value. Lane formulated the concept of cut-off grade optimization for single metal deposit but this method cannot be use in multiple metal deposits. Because in single metal deposits six points are possible candidates for the optimum cut-off grade, in multiple metal deposits an infinite number of points are possible candidates for the optimum cut-off grades. The objective function evaluation of these infinite points is impossible. In this paper, the equivalent grade factor is used to find optimum cut-off grade of multiple metal deposits. First, the objective function is defined for multiple metal deposits and then objective function is converted to one variable function by using equivalent factors. The optimum equivalent cut-off grade of main metal can be found by the optimization techniques such as the Lane algorithm or elimination methods. At final step, the optimum cut-off grades will be determined by interpolation of grade-tonnage distribution of deposit.     

Pit optimisation and life of mine scheduling for a tenement in the Central African Copperbelt

Open pit optimisation and scheduling tasks are an important part of mining ventures that have attracted considerable attention in the mining industry in the past couple of decades. The process of determining the optimum pit significantly impacts the calculation of mine life, which involves huge capital investment. This paper addresses the application of a heuristic algorithm for optimising the pit size and then life of mine scheduling for a copper-cobalt deposit in the Central African copper belt. The resource model was generated using a traditional geostatistical algorithm, specifically the kriging method. The methodology used was to generate a series of optimised nested pits by artificially varying the commodity price and applying a graph closure algorithm. The mine scheduling was generated by combining the solutions of different sub-problems. The deposit is optimised to 9.1?Mt with an average copper grade of 2.03% and cobalt grade of 0.47%. The total NPV generated from the pit is around 495 million US dollars. The results of our proposed algorithm were compared with linear relaxation of the mine scheduling problem. They demonstrated that our proposed algorithm is 30 times more efficient than the linear relaxation problem with an optimality gap of 7.4%.     

市场价格波动与选别式地下开采边界品位控制

理论分析和实例验证表明，选别式开采地下金属矿在完全相同的市场价格形势下，可能采取截然不同的边界品位控制策略。这种情况是由于金属生产和选别式地下开采的特点而引起的。这表现在地下选别式开采的金属产出量受限于采矿准备能力、入选能力（采矿能力或选矿处理能力）和冶炼能力。在金属产出的瓶颈分别出现在这三个不同的生产环节时，随市场价格的升高，若矿山着眼于长期利润目标的最优化，边界品位应分别采取降低、提高和保持不变的控制策略。     

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。     

利用果蝇算法反演概率积分法开采沉陷预计参数

针对概率积分法开采沉陷预计参数反演时存在算法复杂、计算量大等问题,将具有算法简单、计算量小、精度高等特点的果蝇算法引入到概率积分法开采沉陷预计参数反演中,研究了利用果蝇算法反演概率积分法开采沉陷预计参数的基本原理,构造了下沉拟合值与实测值均方差最小的适应度函数模型。结合安徽省某煤矿的实测数据,分别采用果蝇算法、遗传算法以及粒子群算法反演概率积分法开采沉陷预计参数,并以下沉拟合值与实测值的均方差为各算法反演精度的评价标准进行对比分析,结果表明：利用果蝇算法反演出的下沉拟合值与实测值的均方差（33.7 mm）以及相对中误差（1.4%）均小于同类条件下遗传算法、粒子群算法的反演结果,说明果蝇算法适用于反演概率积分法开采沉陷预计参数,对于提高概率积分法开采沉陷预计的精度有一定的参考价值。     

煤矿救援机器人路径规划的蚁群优化算法

煤矿救援机器人执行救援任务时,需躲避水、火、障碍物等危险区域,提升了路径规划的难度,为此提出了煤矿救援机器人路径规划的蚁群优化算法。充分考虑煤矿救援机器人运行过程中的水、火、障碍物等分布,采用栅格法建立机器人路径规划的环境模型,确定栅格环境模型内机器人路径规划问题的目标函数,采用蚁群优化算法求解机器人路径规划问题的目标函数,通过改进信息素规则、限制信息素阈值以及改进转移概率3个方面优化蚁群算法,避免蚁群算法求解全局最优解时陷入局部最优。实例分析结果表明,该算法在满足收敛速度条件下有效规划煤矿救援机器人行驶路径,所规划路径的路径长度、转角数量以及危险度均为最优,为机器人安全作业提供理论依据。     

概率积分法预计参数反演方法研究进展

概率积分法是我国矿山开采沉陷预计的主要方法,其预计的精度直接取决于参数的准确性,如何利用合适的方法准确稳定地求取预计参数是实际应用中的关键问题。全面总结了概率积分法预计参数反演的常用方法并分析了各种方法的优缺点,着重介绍了具有全局搜索能力遗传算法在参数求取中的应用。最后,从概率积分法求参误差、求参准则、求参范围、参数相关性及其模型的非线性等角度,提出概率积分法预计参数求取中存在的问题及需要进一步研究的内容。     

开采区矿山地质环境综合分级定量评价方法

以实现评价矿山地质环境为目的,提出开采区矿山地质环境综合分级定量评价方法。以非金属矿山为研究对象,针对其周边地质环境和生态环境,建立开采区矿山地质环境综合分级定量评价指标体系。采用模糊层次分析算法,对该指标体系内的一级指标和二级指标实施相对重要程度赋值计算后,通过GIS空间分析算法,分析开采区矿山地质环境综合等级赋值频率分布情况,确定矿山地质环境评价的分区阈值,得到开采区矿山地质环境综合分级定量分区结果。实验结果表明,该方法可有效评价非金属开采矿区地裂缝、含水层破坏、地形地貌景观破坏等二级指标等级,可依据二级指标评价结果评价其一级指标等级,具备较好的应用性。     

Transition from open-pit to underground as a new optimization challenge in mining engineering

There are many deposits that have the potential to be mined by a combined method of open-pit and underground. In this manner, the most sensitive problem is the determination of the optimal transition depth from open-pit to underground or vice versa. To calculate this depth, a model based on block economic values of open-pit and underground methods together with the Net Present Value (NPV) attained through mining is first presented. During the model, NPV of open-pit is compared to the value of underground for the similar levels. A hypothetical example is used in order to analyze the model in detail. Based on the assumptions made such as: a discount rate of 15 %, each pair of contiguous level-cuts have to mine during one year, and one level as the height of crown pillar, the optimal transition depth was determined to be equal to 62.5 m. Then, level 6 was considered as the suitable crown pillar. Finally, maximum total NPV of the combined mining was calculated to be 25.54 units of currency.     

智能优化算法在概率积分参数反演中的比较

概率积分法是我国矿山开采沉陷预计的主要方法,其预计的精度直接取决于参数准确性。采用智能优化算法对实测地表沉陷数据反演是获取概率积分法参数的主要方法。为研究优化算法在开采沉陷概率积分参数反演中的应用效果,采用VB语言编程实现了模矢法、遗传算法、粒子群算法、模拟退火算法等常见概率积分参数反演算法,通过构造理论数据分析和比较了这4种算法参数反演的效果,并从运行时间、求参稳定性、搜索性能、抗局部解能力等方面对4种算法进行综合评价。研究结果表明:4种算法参数反演结果精度较高,参数相对误差小于2%,且对观测站中的观测值随机误差、粗差问题具有较强的抗干扰能力。模矢法运行效率高但容易陷入局部解,粒子群算法效率较低,遗传算法和退火算法全局能力强但后期收敛能力较弱。     

Development of risk-informed,performance-based asset management in mining

This paper discusses possibilities of developing a holistic risk-informed, performance-based asset management in mining (RIPBAMM). This process would consist of modelling and probabilistic quantification regarding decision support performance indicators. It assists decision-makers in determining not only which mine improvement investment options should be implemented, but also how to prioritize resources for their implementation based on their predicted levels of profitability. The RIPBAMM approach will complement and integrate existing main mine activities such as exploration, ore body modelling, mine design, planning and scheduling, exploitation (all the phases of the mine life), mineral treatment, cost and market model, operational safety and health, environmental issues, mining equipment reliability and maintenance process, equipment selection model, security, etc. RIPBAMM will involve an integrated assessment of dominant influence factors and performance measures related to mining operations. This process is intended to maximize both net present value (NPV) of the mine, and long-term profitability through a continuous support to a decision-making process. It may be particularly useful while optimizing several mine sites belonging to the same mining company. Initial risk informed asset management (RIAM) applications have been initially developed for the nuclear power industry. Afterwards, this process has been adapted to provide decision-making support to other types of power stations, complex facilities (usually capital-intensive), or even groups of such facilities across a wide variety of industries. RIPBAMM is introducing numerous (stochastic) models and supporting performance metrics that can ultimately be employed in order to support decisions that affect the allocation and management of mine resources (i.e. financial support, employment, scheduling, etc.).     

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.     

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。     

Production scheduling under uncertainty of an open-pit mine using Lagrangian relaxation and branch-and-cut algorithm

ABSTRACT

The life-of-mine optimization of open pit mine production scheduling under geological uncertainty is a computationally intensive process. Production scheduling determines the optimal extraction sequence by maximizing net present value (NPV). In this paper, an algorithm is proposed to schedule an open pit mine under geological uncertainty, where instead of solving the whole problem at once, the production schedule is generated by sequentially solving sub-problems. The sub-gradient method is used to generate the upper bound solution of a Lagrangian relaxed sub-problem. If the upper bound relaxed solution is infeasible, a mixed integer programming is applied to the latter solution. The algorithm is validated by solving six problems and is compared to the linear relaxation of the original production scheduling problem. The results show that the proposed algorithm generates a solution that is very close to optimal, with less than a 3% optimality gap. An application at a copper mine, where geological uncertainty is quantified with geostatistical simulations of the related orebody, shows that all constraints are satisfied and an 11% higher NPV is generated when compared to the corresponding deterministic equivalent of the proposed approach, while a 26% higher NPV is generated compared to a common conventional industry approach.     

基于改进蚁群算法的智能铲运机全局路径规划

以矿井GIS地图为基础建立环境栅格模型,结合改进蚁群算法对智能铲运机在井下环境中的全局路径规划问题进行求解。对基本蚁群算法存在的问题进行改进,分别从路径选择规则、全局信息素更新规则和局部信息素更新规则三方面进行优化。通过仿真实验验证该改进蚁群算法的有效性,并与基本蚁群算法进行比较,结果表明,改进蚁群算法具有较好的稳定性和全局最优性,而且收敛速度较快。该算法可根据已知巷道环境地图得到铲运机的最优路径,有利于智能铲运机的高效工作。