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%.     

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WebGIS露天矿山生产调度系统构建的研究

矿山是一类特殊的地理区域,尤其是露天矿山,一般规模庞大,面积较广,生产管理及调度困难。本文依托安全、智能、高效及可定制的数字化矿山软件体系,将WebGIS技术应用于某露天矿山的管理调度研究,构建了矿山生产调度系统。该系统搭建了统一的生产调度、经营管理和决策支持平台,提高了矿山的生产管理效率,为数字矿山调度平台的建设及应用研究提供参考依据。     

基于WebGIS的露天矿山生产调度系统构建研究

露天矿山一般规模庞大,面积较广,生产管理及调度困难。依托安全、智能、高效及可定制的数字化矿山软件体系,将WebGIS技术应用于某露天矿山的管理调度研究,构建了矿山生产调度系统。该系统搭建了统一的生产调度、经营管理和决策支持平台,提高了矿山的生产管理效率,为数字矿山调度平台的建设及应用研究提供参考依据。     

Optimal mining rates revisited: Managing mining equipment and geological risk at a given mine setup

This paper presents a mixed integer programming formulation dealing with the effective minimisation of risk incurred when optimizing mining production rates in such a way that production targets are met in the presence of geological uncertainty. This is developed through the concept of a “stable solution domain” that provides all feasible combinations of ore and waste extraction for the ultimate pit limit of a given deposit, independent of the geological risk. The proposed formulation provides an optimal annual extraction rate, together with the optimal utilization of a mining fleet and an equipment acquisition program. This solution eliminates unnecessary capital expenses and is feasible under all geological scenarios. The mathematical programming model is detailed and tested at a gold deposit. The results are used as input to a production schedule design and are compared to the schedule generated using a constant mining rate; the comparison shows that about 40% of equipment acquisition can be delayed for 7 years and mill demand still be met, thus maximizing profit and minimizing costs.     

露天矿山生产计划三维可视化编制技术

针对露天矿山生产的基本特征及矿山对编制生产进度计划方面的要求,对计划编制的关键技术及三维可视化环境下的系统结构进行了研究。以三维可视化建模与设计技术作为基础构建3D数据库平台,将露天生产对象分解成任务单元,然后对任务进行属性赋值、分解、排序,再通过各种统计方法,生成各种计划进度表。最后通过工程实例验证了本技术的可行性及其优越的性能,结果表明三维可视化技术应用于矿山生产进度计划编制中是高效合理的,在三维环境下进行可视化编制,使复杂的生产进度计划编制变得清晰明了,极大降低了露天矿生产进度计划编制的复杂性和难度,同时也可以对我国矿山企业的数字化起到一定的推动作用,具有积极的现实意义。     

多金属露天矿多目标生产计划优化问题建模及求解算法

针对多金属露天矿山生产计划优化问题难以建模、求解复杂等问题,从多种金属元素、采掘运输成本以及矿石品位三个角度出发,综合考虑矿石产量、品位波动、矿石资源利用率、开采和处理能力以及回采率等多种影响因素,构建了一个多金属露天矿多目标生产计划模型。受粒子群算法启发,提出一种改进狼群算法（IGWO）对模型进行求解,并引入反向学习策略和非线性收敛策略来提高算法的求解效率。以国内某露天矿的实际生产为例,分别利用粒子群算法（PSO）、灰狼算法（GWO）和IGWO算法对模型进行求解对比。结果表明：该生产计划模型更加符合露天矿多种矿产资源综合开采利用的实际需求,IGWO算法较PSO算法运行速度上提高了71%,在求解精度上提高16%。该生产计划方案对多金属露天矿山矿产资源综合利用及精细化排产具有重要的指导意义,可促进企业可持续发展。     

基于免疫算法的三道庄露天矿车辆调度优化

分析露天矿车辆调度问题,建立求解矿山车辆调度问题的数学模型。矿山车辆调度问题实际上属于NP完全问题,建立多目标优化模型来求解,即解决总运量最小问题。最后,通过免疫算法在三道庄露天矿车辆调度优化中的应用实例表明,本算法可以快速求得优化解,是求解车辆调度问题的一种有效算法。     

露天矿计划阶段内离散块体物料运距预测算法

矿岩运距是衡量露天矿山卡车运输经济性的重要指标之一,但多年因受运输系统复杂、多变等多种综合因素限制,在进度计划编制期间进行逐条带的运距计算问题一直并未得到有效解决。特别是需要进行离散化的物料规划时,传统逐阶段的运距量测方法无法对离散块体进行逐个推估。因此,为有效解决计划阶段内离散块体物料运距计算问题,根据露天矿外排土场出入口选址及排土运输干线相对固定等空间特征,将非线性预测理论、因子分析法等技术方法应用于实际的矿山优化问题中,研究了排土场计划阶段内块体运距波动变化的主要控制因素;结合外排土场内运距波动变化的影响要素,提出了采用加权最小二乘支持向量机技术(WLS-SVM)拟合非线性运距曲线的预测算法,并对权向量、核参数等主观经验指标进行了动态修正,以实现对计划阶段内(两阶段工程位置间的)离散块体物料过程运距的时变预测;最终,利用拟合出的时变曲线,实现两连续工程位置间逐个物料块体运距的高效计算。实验结果表明:预测算法的误差期望分别为:训练集0. 93 m,测试集0. 84 m,且在实验中表现出模型精度易受样本规模影响的特性,且当样本规模N90时,可控制绝对误差水平稳定在0. 8%～1. 2%。结论表明:试图应用非线性预测理论处理计划阶段内缺乏时变路网条件的运距预测问题是可行的,提出的算法模型对解决计划阶段内的逐块体运距赋值问题具有现实有效性。常规的露天矿山运输优化问题其优化目标和特征参数之间往往存在紧密耦合关系,无法直接应用特定的优化、规划模型进行计算求解,尝试采用全新的解耦思想和求解思路对于有效解决露天矿山运输优化问题是十分有益的,也应该是今后露天矿山系统工程学科研究的热点问题之一。     

考虑生态成本的露天煤矿生产计划优化

在给定的露天矿境界中做生产计划,就是确定每年采场的推进位置、采剥量。不同的生产计划,每年的采剥量和采场推进位置也就不同,造成每年采场、排土场的破坏面积以及每年的污染物排放量不同,从而引发不同程度的生态破坏。鉴于此,首先基于一个已知最优境界,使用锥体排除法产生一系列地质最优开采体并进行动态排序;然后采用动态规划法对某大型露天煤矿设计多个生产方案,同时根据矿山环境破坏的时空顺序,建立矿山生态足迹和生态成本计算模型,评估生产方案与环境压力之间的相互影响关系。研究表明,不同的生产设计方案对矿山生态冲击不同,且生态成本占矿山总净现值比例较大,同时生态成本对优化方案的选择产生影响。     

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。     

Stochastic optimisation of long-term block cave scheduling with hang-up and grade uncertainty

Abstract

Mass mining methods provide alternatives in developing deeper and lower-grade mineral deposits. Consequently, block cave mining has been increasingly popular mass mining method, especially for large copper deposits currently being mined by open pit methods. This study adopts similar concepts as in stochastic open pit production planning to the planning of block cave mines, to evaluate their effectiveness in a different approach to mass mining. The main contribution of this study is the incorporation of the uncertainty of delays from hang-ups and grades directly into the production scheduling process of a cave mining operation. Hang-up uncertainty relates to the uncertainty linked to the occurrence of ore that clogs the production draw points. This clogging causes time delays in the production cycle leading to tonnage losses and additional costs. Grade uncertainty is incorporated by means of stochastic orebody simulations. Both uncertainty sources are directly linked to the extraction decisions and influence the optimized schedules. The proposed stochastic integer programming model is applied to the optimization of the long-term schedule of a large-scale, low-grade copper deposit by taking into account hang-up delays in block caving. The results of the optimization maximizing net present value clearly show the capability of the formulation to mitigate the effects of both grade and hang-up uncertainty.     

露天矿矿体计算机模型的建立

露天矿矿体计算机模型的建立是进行矿床开采境界优化及制定矿山生产计划的基础。为实现矿山生产现代化管理，德兴铜矿建立了大型露天矿山矿体计算机模型，并获得成功应用，对类似矿山具有参考意义。     

露天矿山开采境界动态优化圈定

按不同边界品位对矿床模型进行优化参数属性赋值,形成一系列静态价值模型,运用动锥法及L-G法进行初步优化,获得一系列静态境界方案,通过编排进度计划等方式将时间属性植入矿床块体模型,计算不同境界方案的年现金流,经贴现获得净现值(NPV),综合比较各方案NPV及资源回收情况确定最终方案。以某大型露天铜矿为例,利用矿业软件Surpac及进度计划软件Min-esched实现了最终境界的动态优化圈定,结果显示,原静态最优方案为不可行方案,而动态优化最终方案在经济效益上占绝对优势。     

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.     

Oil sands mine planning and waste management using mixed integer goal programming

Strategic mine planning and waste management are an important aspect of surface mining operations. Recent environmental and regulatory requirements make waste management an integral part of mine planning in the oil sands industry. The research problem here is determining the order of extraction of ore, dyke material and waste to be removed from a predefined ultimate pit limit over the mine life that maximises the net present value of the operation. We have developed, implemented, and tested a proposed mixed integer goal programming theoretical framework for oil sands open pit production scheduling with multiple material types. The formulation uses binary integer variables to control mining precedence and continuous variables to control mining of ore and dyke material. There are also goal deviational variables and penalty costs and priorities that must be set up by the planner. The optimisation model was implemented in TOMLAB/CPLEX environment. The developed model proved to be able to generate a uniform schedule for ore and dyke material. This is in line with recent regulatory requirements by Alberta Energy Resources and Conservation Board (Directive 074) which requires oil sands mining companies to develop life of mine plans which ties in to their in-pit tailings disposal strategy. It also provides a practical mining sequence that is consistent with mining oil sands deposit. Similarly, tradeoffs between achieving a goal and maximising NPV can be made.     

基于仿真的矿山生产计划优化研究与工程应用

煤矿生产是由采掘、洗选和装车运输等多个环节组成的复杂生产流程。针对矿山企业实际生产过程中调度参数优化问题,根据矿山生产任务和实际生产情况,以矿山资源消耗最小为优化目标,以采场地质因素、企业销售订单和各环节生产能力为约束条件建立多目标优化模型。通过构建矿山生产流程仿真平台和生产参数优化实现模型求解,最终利用生产调度实现生产资源的最优化配置。结果表明,基于仿真的生产计划优化方法能够较好地应用于生产实践。     

基于距离的开采区域规整性测度及其几点性质

基于距离的开采区域规整性测度是评价露天矿开采区域连续规整程度的一种指标,将其加入到一般的露天矿生产调度模型当中,可获得现实可行的露天矿生产调度方案。用定理的方式证明了这种开采区域规整性测度具有3点性质。即方形优先性、可平移性和可旋转性,从而从另一个角度证明了它的合理性,并为它的应用奠定了数理基础。     

SURPAC境界优化功能在露天矿山的应用

露天矿山的开采境界设计对矿山的盈利水平和生产能力有十分重要的影响。以辽宁省某露天铁矿采矿设计为例,介绍了SURPAC三维设计软件对露天矿山终了境界进行优化设计的全过程。通过建立地质数据库、表面模型、终了模型和矿体模型,并将其作为新建块体模型的约束条件,通过SURPAC实现矿山设计的立体呈现,并经运算得出露天境界内分水平矿岩量。分析采用SURPAC软件境界优化前后经济指标的变化情况,为矿山企业生产决策工作提供参考,对露天矿山的境界优化设计有一定的借鉴意义。     

基于ISSA-XGBoost模型的多特征融合露天矿卡车行程时间预测

针对露天矿运输系统卡车行程时间预测问题,提出了一种基于特征选择及改进麻雀算法优化XGBoost的露天矿卡车行程时间预测模型。模型充分考虑了卡车特征、道路特征、气象特征以及时间特征对卡车行程时间的影响,并使用皮尔逊系数法深入分析影响因素的贡献度。针对麻雀算法中全局搜索能力薄弱的问题引入反向学习和螺旋搜索策略,以提高算法的收敛性能。最后,使用改进的麻雀算法对XGBoost的关键参数进行寻优,进而构建露天矿卡车行程时间预测模型。选取国内某大型露天矿卡车调度系统采集的数据进行仿真模拟,并将所提出模型与SVM、BP、RBF和RF等其他机器学习模型进行对比。结果表明：所提出模型的预测误差均低于其他模型,相关系数可达0.981 9。开发的模型和分析结果可以极大地帮助决策者规划、运营和管理更高效的露天矿运输系统。