Choosing the optimum cut-off grade

Mining Hydrogeological Problems in Underground Excavation of Vein-Typed Gold Deposit under Hydraulic Inter-Connection with Surface Water Body - 3. Analysis of Groundwater Inflow and Preliminary Scheme of Decision Making Process.

Conference Paper

Full-text available

Sep 2017

This paper is sequel to and is a continuation of several previous papers (Widodo, 2013, 2015, 2016a, and 2016b) on the mining hydrogeological problems of vein-typed deposit interconnected with surface water bodies. Widodo (2013) described the main problem of groundwater management in underground mines, while Widodo (2015) provided a comprehensive problem-solving frame work. Widodo (2016a) explained the principles of gold resource estimation and Widodo (2016b) described the engineering hydrogeology philosophy of groundwater management. In this paper will be discussed the analysis of groundwater inflow into the underground mining facility. This is important since the solution used to solve groundwater management problems in underground mining is based on the trade-off principle (Widodo, 2013), so optimization becomes important and is the main tool of decision making process, in which the economic potential of gold resources compared to the cost of groundwater management in underground mining facilities. The hydraulically interconnected ore body with surface water bodies acts as an aquifer with unlimitted recharge. Groundwater analysis into underground mining facilities was carried out using the PARIKESIT software developed by Nurcahya (2017) based on finite element method, and applied the McDonald and Harbaugh (1988) formula to drain. Groundwater problems inflow into underground mining facilities can be categorized into drain phenomena. From the analysis of groundwater inflow is known, that the increase in total drainage discharge in the underground mining infrastructure is directly proportional to the depth of crosscut. At each crosscut depth, the drain discharge on the shaft and crosscut decreases every increase of iteration, while the drain discharge out of the ore body is constant. PARIKESIT is good enough to calculate groundwater inflow from hydraulically interconnected ore bodies with surface water bodies into underground mine infrastructure. Based on the result of verification with Visual ModFlow software, it can be concluded that the estimated flow rate drain using PARIKESIT is almost the same as the estimated flow rate drain using Visual ModFlow software. The decision making process uses optimizer based on genetic algorithm (GA), which always results in global solutions. In this case, optimization has multi-objective function, because there are two objectives that are maximizing the gold resources and minimizing the cost of groundwater management. Acting as a decision variable in this case is the depth of the initial crosscut or the deepest depth of the crosscut on the underground mining system based on the overhand principle.

Mining Hydrogeological Problems in Underground Excavation of Vein-Typed Gold Deposit under Hydraulic Inter-Connection with Surface Water Body 3. Analysis of Groundwater Inflow and Preliminary Scheme of Decision Making Process.

Preprint

Sep 2017

This paper is sequel to and is a continuation of several previous papers (Widodo, 2013, 2015, 2016a, and 2016b) on the mining hydrogeological problems of vein-typed deposit interconnected with surface water bodies. Widodo (2013) described the main problem of groundwater management in underground mines, while Widodo (2015) provided a comprehensive problem-solving frame work. Widodo (2016a) explained the principles of gold resource estimation and Widodo (2016b) described the engineering hydrogeology philosophy of groundwater management. In this paper will be discussed the analysis of groundwater inflow into the underground mining facility. This is important since the solution used to solve groundwater management problems in underground mining is based on the trade-off principle (Widodo, 2013), so optimization becomes important and is the main tool of decision making process, in which the economic potential of gold resources compared to the cost of groundwater management in underground mining facilities. The hydraulically interconnected ore body with surface water bodies acts as an aquifer with unlimitted recharge. Groundwater analysis into underground mining facilities was carried out using the PARIKESIT software developed by Nurcahya (2017) based on finite element method, and applied the McDonald and Harbaugh (1988) formula to drain. Groundwater problems inflow into underground mining facilities can be categorized into drain phenomena. From the analysis of groundwater inflow is known, that the increase in total drainage discharge in the underground mining infrastructure is directly proportional to the depth of crosscut. At each crosscut depth, the drain discharge on the shaft and crosscut decreases every increase of iteration, while the drain discharge out of the ore body is constant. PARIKESIT is good enough to calculate groundwater inflow from hydraulically interconnected ore bodies with surface water bodies into underground mine infrastructure. Based on the result of verification with Visual ModFlow software, it can be concluded that the estimated flow rate drain using PARIKESIT is almost the same as the estimated flow rate drain using Visual ModFlow software. The decision making process uses optimizer based on genetic algorithm (GA), which always results in global solutions. In this case, optimization has multi-objective function, because there are two objectives that are maximizing the gold resources and minimizing the cost of groundwater management. Acting as a decision variable in this case is the depth of the initial crosscut or the deepest depth of the crosscut on the underground mining system based on the overhand principle.

OPTIMASI VALUASI EKONOMI ENDAPAN NIKEL LATERIT MEMPERHITUNGKAN BIAYA LINGKUNGAN: OPTIMIZATION OF THE ECONOMIC VALUATION OF LATERITIC NICKEL DEPOSITS CONSIDERING ENVIRONMENTAL COSTS

Article

Full-text available

Jun 2022

Optimasi valuasi ekonomi mineral bertujuan untuk menentukan nilai sekarang bersih maksimum suatu proyek selama umur tambang. Model optimasi valuasi ekonomi dalam penelitian ini adalah pengembangan dari model Lane (1988) dan Sasongko (2013) dengan memperhitungkan biaya lingkungan serta mengacu rerangka aliran kas. Metode penelitian ini meliputi tahapan sebagai berikut: (1) pemodelan dan estimasi sumber daya, (2) pemodelan valuasi ekonomi mineral, (3) penentuan solusi model, dan (4) valuasi ekonomi mineral. Pemodelan sumberdaya dalam bentuk model blok ukuran 25 m x 25 m x 1 m. Estimasi kadar blok menggunakan metode interpolasi inverse distance weighting (IDW). Pemodelan optimasi valuasi ekonomi dalam penelitian ini adalah pemodelan dalam rerangka aliran kas dengan mempertimbangkan biaya lingkungan dan kebijakan pemerintah seperti pajak, royalti, dan depresiasi. Optimasi cut-off grade adalah suatu usaha untuk menentukan kadar optimum yang akan menghasilkan keuntungan atau nilai sekarang bersih (net present value, NPV) maksimum. Solusi model dalam hal ini meliputi optimasi cut-off grade untuk optimasi profit dan optimasi NPV. Solusi model untuk menentukan kadar batas optimum tergantung pada batasan kapasitas penambangan, konsentrasi, dan pemurnian. Penentuan solusi model optimasi kadar batas menggunakan metode analitik. Pada studi kasus, estimasi sumberdaya terukur sejumlah US$4.253.566 ton bijih nikel. Pada laju penambangan konstan pada kadar batas optimum 0,95 %, maka umur tambang 4,85 tahun dengan NPV US$811.248.447. Optimasi valuasi ekonomi dengan indikator NPV, umur tambang 4,44 tahun dan dihasilkan NPV maksimum sebesar US$841,596.460. Nilai cut-off grade berbeda-beda di setiap tahun penambangan, yaitu tahun ke-1 kadar 0,99%; tahun ke-2 kadar 0,99%; tahun ke-3 kadar 0,98%; tahun ke-4 kadar 0,97%; tahun ke-5 kadar 0,95%. Optimasi valuasi ekonomi NPV memiliki nilai lebih besar dan waktu yang lebih pendek, dibandingkan dengan optimasi keuntungan (profit).

What is the optimal cutoff surface for ore bodies with more than one mineral?

Article

Jan 2022
OPER RES LETT

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.

A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex

Preprint

Full-text available

Dec 2021

In techno-economic concern, cut-off grade (COG) optimization is the key for efficient mineral liquidation from the huge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on discrete multi-value dynamic programming (MDP) has been developed to calculate the global optimum COG of a large-scale open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome the limitations of straightforward classical techniques in determining the optimum COG. This discrete COG-MDP model is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities to achieve the maximal global Net Present Value (NPV). A high-level programming language (Python) has been used to develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamic variables. This model can generate results in polynomial-time from the complex of mining, milling, and smelting and refining system corresponding to various limiting conditions. The prime objective considered in the model is to optimize the COG of a metalliferous deposit. A working open-pit copper mining complex from India has been used to validate the model. In this study, the optimum COG for the Malanjkhand copper deposit has been found to be (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609, 21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present value gradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms.

A sequentially advancing algorithm based on multi-value dynamic programming for the cut-off grade optimization in open-pit metalliferous deposits

Preprint

Full-text available

Dec 2021

In techno-economic concern, cut-off grade ( COG ) optimization is the key for efficient mineral liquidation from the huge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on exact multi-value dynamic programming (MDP) has been developed to determine the optimum COG of an open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome the limitations of straightforward classical techniques in determining the optimum COG . This discrete COG-MDP model is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities to achieve the maximal Net Present Value (NPV). A high-level programming language (Python) has been used to develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamic variables with a precision value of 0.01% in grade bins. This model can generate results in polynomial-time from the complex mine, mill, and smelter and refinery system corresponding to various limiting conditions. The prime objective considered in the model is to optimize the COG of a metalliferous deposit. The model validation has been done using a real-life case study of an open-pit copper mine in India (Malanjkhand Copper Mine, HCL), considering the fixed yearly output of the mining, milling, and smelting and refining. In this study, the optimum COG for the Malanjkhand copper deposit has been found to be (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609, 21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present value of net cash-flow grows in the early years, peaks at a specified mid-life time, and then drops as the reserve is depleted. The present value gradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms.

Applications of Integer Programming and Decomposition to Scheduling Problems: the Strategic Mine Planning Problem and the Bin Packing Problem with Time Lag

Thesis

Feb 2021

Orlando Rivera-Letelier

In scheduling problems, the goal is to assign time slots to a set of activities. In these problems, there are typically precedence constraints between activities that dictate the order in which they can be carried out and resource constraints that limit the number that can simultaneously be executed. In this thesis, we develop mixed integer programming methodologies, based on decomposition methods, for two very different classes of scheduling problems. These are the Strategic Open Pit Mine Planning Problem (SOPMP) and the Bin Packing Problem with Time Lags.Given a discretized representation of an orebody known as a block model, the SOPMP that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. These problems are known to be very difficult due to the large size of real mine planning problems (eg, millions of blocks, dozens of years). They are also very important in the mining industry. Every major mining operation in the world must solve this problem, at the very least, on a yearly basis.In this thesis, we tackle the SOPMP in Chapters 2 and 3.In Chapter 2 we begin by studying a lagrangean algorithm developed by Dan Bienstock and Mark Zuckerberg (henceforth, the BZ algorithm) in 2009 for solving the LP relaxation of large instances of SOPMP. In this study we generalize the classes of problems that can be solved with the BZ algorithm, and show that it can be cast as a special type of column generation algorithm. We prove, for general classes of mixed integer programming problems, that the BZ relaxation provides a bound that lies between the LP relaxation and Dantzig-Wolfe bounds. We further develop computational speed-ups that improve the performance of the BZ algorithm in practice, and test these on a large collection of data-sets. In Chapter 3 we deal with the problem of computing integer-feasible solution to SOPMP. Using the BZ algorithm developed in Chapter 2, we develop heuristics for this. In addition, we develop pre-procesing algorithms that reduce problem size, and embed the BZ algorithm in a branch-and-cut framework that makes use of two new classes of cutting planes. When comparing the value of the heuristics to the LP relaxation bound, the average gap computed is close to 10\%. However, when applying the pre-processing techniques and cutting planes, this is reduced to 1.5\% at the root node. Four hours of branching further reduces this to 0.6\%.In Chapter 4, the BPPTL is presented. This is a generalization of the Bin Packing Problem in which bins must be assigned to time slots, while satisfying precedence constraints with lags. Two integer programming formulations are proposed: a compact formulation that models the problem exactly, and an extended formulation that models a relaxation. For two special cases of the problem, the case with unlimited bins per period and the case with one bin per period and non-negative time lags, we strengthen the extended formulation with a special family of constraints. We propose a branch-cut-and-price (BCP) algorithm to solve this formulation, with separation of integer and fractional solutions, and a strong diving heuristic. Computational experiments confirm that the BCP algorithm outperforms solving the compact formulation with a commercial solver. Using this approach we were able to optimally solve 70\% of a class of previously open instances of this problem.

A mixed integer programming based cut-off grade model for open-pit mining of complex poly-metallic resources

Article

Mar 2021
RESOUR POLICY

The mineral supply chain in an ideal open-pit mining operation constitutes a set of sequential stages including a surface mine or an open-pit, a processing plant and a refinery or market. Cut-off grade defines the flow of materials from the mine to subsequent stages within this mineral supply chain. This underlines the significance of cut-off grades in establishing the economic viability of an operation. However, only heuristic methods are available for defining the cut-off grade policy for complex mineral resources (orebodies) that constitute multiple economic minerals. This article proposes a new mixed integer programming based mathematical model that generates an optimal cut-off grade policy for open-pit mining operations that mine, process and refine or market multiple metal products. An implementation of the new method in three separate case studies reflects better performance (i.e., 24%, 36% and 27% higher net present value) against available heuristics.

Lane’s Algorithm Revisited

Article

Oct 2020

In 1964, Kenneth Lane proposed an algorithm to optimize the production schedule of a single-metal, single-processor open pit mine. For this, he proposed a policy based on varying, over time, the so-called “cutoff grade”—or grade threshold used to determine if extracted material should be ore (processed material) or waste (thrown away). Lane’s algorithm had a profound impact on the mining industry. However, though it has been used in multiple commercial software systems and has traditionally been taught to every aspiring mining engineer, it is widely considered a heuristic, and little is known regarding the quality of the solutions it produces. In this paper, we formally study Lane’s problem. We show that Lane’s algorithm can be viewed as an approximate dynamic programming scheme and that Lane’s optimality conditions can be formally derived in two different ways: by considering a variant of the problem where the future value function is linearly approximated or by deriving the optimality conditions of a continuous-time version of the problem. We further show that Lane’s algorithm can naturally be extended to this continuous-time version of the problem and that when this algorithm converges, it converges to an optimal solution. Finally, through a reformulation, we show that Lane’s original problem can be solved using convex mixed-integer programming. Though hypothetical counterexamples can be constructed, computational experiments prove that Lane’s algorithm can produce the optimal solution in every real-world data set tested, thereby lending solid support for its practical application. This paper was accepted by Chung Piaw Teo, optimization.

Algorithmic Optimization of an Underground Witwater- srand-Type Gold Mine Plan

Article

Nov 2020

In the mining environment, mine planning is complicated by the presence of unfavorable environmental conditions, limited knowledge of the shape and size of the deposit, ore body characteristics, and volatile market conditions. In this paper, we propose a top-down algo- rithmic approach to strategically optimize the cutoff grade and net present value (NPV), and implement its solutions at the operation level, while simultaneously mitigating operation risks, to maximize the life of an ultra-deep gold mine from the Witwatersrand Basin, South Africa. To date, the Witwatersrand Basin has contributed about 28% of the worldÕs total gold supply from a series of Mesoarchaean quartz pebble conglomerate units (referred to as reefs). Through a quantitative analysis using algebraic and stochastic methods, we ranked mining variables in terms of their margin sensitivity and impact/adjustability efficacy. The results of this study showed the following. By using our proposed approach, an underground mine plan can be optimized by focusing on few key variables. Strategic mining of combi- nations of high-grade panels with low-grade panels and counter-balancing their risk profiles can yield optimal executable mine plan results (i.e., higher NPV, ideal profit margin, and lower risk) without sterilizing a given mineral resource for underground mining operations.

Mining Optimization Laboratory (MOL) Annual Report Seven 2015/2016, © MOL, University of Alberta, Edmonton, Canada, 13 papers, 240 Pages

Technical Report

Full-text available

Sep 2016

This year, we have prepared a report including 13 papers. We continue to update all the research results on the MOL webpage www.ualberta.ca/mol on the members section. Sponsors have access to current and past research results, publications, prototype software, and source code. Let’s review the contributions in the MOL Report Seven (2015/2016) by considering some of the main contributors. In paper 101, Shiv presents a simulation optimization approach for uncertainty based short term planning and proactive decision making, which provides substantial economic and operational gains. An optimization tool is presented in this paper to achieve uniform desired grade and tonnage feed to processing plants, and maximum production to comply with medium to long term roduction schedule with minimal shovel movement within a simulation model. The system considered in his model is an open pit mine with truck-shovel operations. The system includes trucks, shovels, plant crushers, waste dumps, haul road network and mining faces (scheduling polygons) with different material types based on the medium to long term production schedule. Shiv also details the development of simulation and optimization models in paper 203. He presents the implementation of the framework on an iron ore mine case study for the verification through scenario analysis. The simulation optimization framework/tool uses a discrete event simulation of mine operations, which interacts with a goal programming based mine operational optimization tool (MOOT), to capture the performance and develop uncertainty based short term schedule. Navid presents an application of cut-off grade optimization to oil sands production scheduling and waste management in paper 102. His research investigates the impact of dynamic cut-off grade on the NPV of an operation. The objectives are to: 1) determine the life of mine optimum cut-off grade profile and corresponding ore tonnages to maximize the NPV of the operation; 2) determine the dyke material schedule for dyke construction; and 3) assess the impact of stockpiling and stockpile reclamation with limited duration. Scenarios investigated includes: no stockpiling; stockpiling and reclaiming at the end of mine life; and stockpiling with limited reclamation duration. The model generates an optimum cut-off grade policy and a uniform production schedule for ore and dyke material over the mine life. The benefit of using the stockpile with two reclamation methods was presented. Reclaiming the stockpiled material after the mining operation resulted in an increased total ore tonnage. Also, the reclamation of stockpiled material simultaneously with the mining operation increased the total ore tonnage as well as maintaining the average head grade required by the processing plant. By maintaining the average head grade, the total NPV generated in the third scenario was higher than the second scenario. Dylan has been working towards developing a conceptual framework for managing mineralized mine waste as a future resource in paper 103. Currently, even though most natural resources are non-renewable, the majority of mineral resources are not mined until physical depletion, but rather current economic depletion resulting in valuable minerals being left behind. The main focus of this research is to: a) propose and implement a conceptual framework for a waste management system that enables reprocessing of mineralized waste directly by the processing plant; and b) propose legislative recommendations for life of mine waste management particularly for non-renewable natural resources. The framework suggest that by reprocessing the mineralized waste when metal prices fluctuate favourably and processing technology advances, less metal will be left behind resulting in sustainable mining operations. Ahlam started her PhD research in open pit mine planning and waste management optimization. Her research will develop a multi-objective stochastic mathematical programming model considering grade uncertainty. She has done a literature review on open pit mine planning and waste management and oil sands mining (paper 104). The paper discusses heuristic, meta-heuristic and deterministic optimization approaches, as well as application of artificial intelligence and uncertainty-based approaches to mine planning and waste management. Limitations of current mine planning models have been outlined. Mohammad and Shiv developed a framework that takes production and maintenance schedules, haul road network, truck list and allocation strategy, shovel list, operation control parameters, and other probability distribution functions as inputs through spreadsheets and produces the reports required for analyzing the system performance and comparing expansion and modification scenarios. In paper 201, they explain all the steps required to develop and implement a simulation model by automating the procedure through programming and flexible model building and concludes by presenting normalized operation versus simulation statistics and plots to show the accuracy and reliability of their simulation model. Ali presents a truck-shovel simulation reliability analysis with embedded dispatch optimizer in paper 202. A general reusable discrete-event simulation tool is developed and verified to analyze the behavior of open pit mining operations. The simulation tool imitates the truck-shovel operation and its interaction with the mining fleet management systems. The simulation model is linked to the mine production schedule. The developed simulation tool accurately monitors the system’s major KPIs. The simulation model is run for predetermined number of replications over the desired planning time horizon to generate tight half-widths around the monthly and shift-based KPIs with high confidence level. The tool includes a thorough implementation of a dispatching logic which mimics real-world dispatching systems in allocating trucks to the neediest shovels on the shortest travel path. Moreover, a new algorithm is developed for truck allocation by MOL and was implemented in the system. Comparing the new algorithm with the common real world dispatching systems on a case-study provides a 10% improvement in the production of the operation. Firouz has been carrying out research on block-cave production scheduling using mathematical programming (papers 301 and 305). He models the production scheduling in block-cave mining to maximize the net present value of the project using MILP and also implements MIQP as non-linear tool to minimize the difference between the objective and the target tonnage of the mining project considering the related constraints of the operations. He uses mathematical programming as a strong tool to model the operation in block cave mining with the objective function in which minimizes the deviation of extraction from drawpoints. The problem was first formulated as a quadratic programming model then the problem was converted to a linear programming with absolute values. Technical and operational constraints such as mining capacity, average grade for production, continuous mining, drawpoint’s life, draw control and number of active drawpoints are considered for the operations. Testing both the quadratic and the linear model with absolute values for a real case mining project shows that the linear model with absolute values is easier and faster to solve. In paper 302, Amir discusses the caving process and all effective parameters. Then, he introduces the interaction matrix based on the rock engineering system (RES) to study the influencing parameters in rock mass fragmentation. The interaction matrix analyzes the interrelationship between the parameters affecting rock engineering activities. The interaction matrix for influencing parameters are established and coded by ESQ (Expert Semi Quantitative) approach. As a result, the high dominant or subordinate, and also the most interactive parameters, are introduced. The proposed approach could be a simple but efficient tool in the evaluation of the parameters affecting the fragmentation of rock mass in block-cave mines and as a result, useful in decision-making under uncertainties. Saha has been working towards development of a methodology to find the best extraction level under grade uncertainty for block-cave mining (paper 303). The main goal of the study is to develop a framework to find the best level of extraction under grade uncertainty. In this paper, several realizations are modelled by using geostatistical studies to consider the grade uncertainty. After determining the best extraction level, the production schedule is generated for the best advancement direction and in presence of some constraints at the extraction level using a mixed-integer linear model. Efrain, presents a methodology based on Sequential Gaussian Simulation (SGS) to obtain the optimum drawpoint spacing in paper 306. The optimized drawpoint spacing is used to maximize the profit since the extraction layout is highly essential for the economics of block caving. This study is opening a new horizon for using “All Realizations All the Time” as a new approach to solve one of the trickiest elements of blocks caving. He also compares recoverable reserves between simulation and kriging for block caving in paper 304. He conclude that despite the fact that the block caving design depends on many parameters and constraints and its evaluation is very challenging, an efficient extraction layout could be obtained by using a set of realizations. Managing a huge number of realizations is still a bit time consuming, hence the usage of 40 to 100 realizations is recommended. Moreover, hardware and software have been improving over the years.

An optimal cut-off grade policy under diverse stockpile handling strategies in open-pit mining operations

Article

Jul 2020

An optimal cut-off grade policy maximises the net present value of an open-pit mining operation and defines a schedule of cut-off grades and the corresponding supply of materials to various destinations. Generally, the cut-off grades are dynamic and decline with the exhaustion of reserves from one year to the next. Thus, stockpiling of the low-grade uneconomic material during earlier years becomes an option to process or blend stockpiled material during later years of mine life. Stockpiling is an established practice in the mining industry and given its significance; as an alternative to traditional cut-off grade models, this article presents a mixed integer programming-based mathematical model that offers an optimal cut-off grade policy with an option to stockpile using three different strategies. The implementation of the new formulation using a case study mining operation available in literature reveals the value of the new model.

ANALISIS PENENTUAN KADAR BATAS OPTIMAL (OPTIMUM CUT-OFF GRADE) DENGAN METODE LANE: STUDI KASUS PENAMBANGAN EMAS BAWAH TANAH

Article

Full-text available

Mar 2020

ABSTRAKKonservasi mineral akan tercapai manakala semakin banyak cadangan mineral tertambang dan meninggalkan sesedikit mungkin material waste. Untuk mencapai hal tersebut salah satu cara yang dapat ditempuh adalah menentukan jumlah cadangan berdasarkan kadar batas yang optimal (optimum cut-off grade). Dalam penentuan optimum cut-off grade, model matematis yang dapat dipergunakan adalah model/persamaan Lane. Metode Lane akan memaksimalkan nilai Net Present Value (NPV) dengan mempertimbangkan 3 variabel, yaitu; variabel ekonomi (harga komoditas dan biaya), distribusi kadar pada endapan, dan kapasitas maksimum pada tahapan penambangan (mining, milling, and refinery). Model Lane biasa diterapkan dalam tambang terbuka, namun dalam penambangan bawah tanah sulit untuk diterapkan. Dalam peper ini akan dikaji penerapan Model Lane dalam penentuan optimum cut-off grade pada penambangan urat (vein) emas bawah tanah dengan metode cut-and-fill. Hasil simulasi menunjukkan nilai optimum cut-off grade yang dinamis dalam memaksimalkan NPV dan nilainya lebih besar dari break even cut-off grade.Kata Kunci: model Lane, optimum cut-off grade, tambang bawah tanah ABSTRACTMineral conservation will be obtained if more mineral reserves are extracted and leaves less waste as possible. One of the methods to achieve those condition is determining the total minable reserves based on the optimum cut-off grade. Optimum cut-off grade can be estimated using Lane Model. Lane Model will maximize the Net Present Value (NPV) by considering 3 variables, i.e; economic variables (commodity prices and costs), grade distribution of deposit, and maximum capacity of each stage of production (mining, milling, and refinery). Lane models are usually applied in open-pit mines, unfortunately it is difficult to apply for underground mining unless some there are some modifications. This paper will examine the application of the Lane Model in determining the optimum cut-off grade in underground gold mine using cut-and-fill method to extract vein type deposit. Simulation result show dynamic optimum cut-off grade which maximizing NPV and generally greater than the break-even cut-off grade.Key Words: Lane model, optimum cut-off grade, underground mine

Simultaneous stochastic optimization of production sequence and dynamic cut-off grades in an open pit mining operation

Article

Jun 2020
RESOUR POLICY

An open pit mining operation is a complex system that constitutes several components or processes. An optimal production sequence that defines timing of extraction and a dynamic cut-off grade policy that defines the supply of materials from sources to destinations within the system are crucial to the success of an operation. In current practice, separate sequencing and cut-off grade models achieve these important milestones as part of strategic planning. This paper presents a mathematical model that derives the optimal extraction sequence and cut-off grade policy simultaneously considering grade uncertainty and stockpiling. A framework of genetic, maximum flow and cut-off grade algorithms solves this complex non-linear problem. An application of the method at realistic copper and gold mining operations reveals the value (up to 29% increase in discounted value) of stockpiling as well as risk quantification under uncertainty.

A stochastic cut-off grade optimization model to incorporate uncertainty for improved project value

Article

Full-text available

Mar 2019

Cut-off grade is a decision-making criterion often used for determining the quantities of material (ore and waste) to be mined, ore processed, and saleable product. It therefore directly affects the cash flows from a mining operation and the net present value (NPV) of a mining project. A series of different cut-off grades that are applied over the life of mine (LOM) of an operation defines a cut-off grade policy. Due to the complexity of the calculation process, previous work on cut-off grade calculation has mostly focused on deterministic approaches. However, deterministic approaches fail to capture the uncertainty inherent in input parameters such as commodity price and grade-tonnage distribution. This paper presents a stochastic cut-off grade optimization model that extends Lane's deterministic theory for calculating optimal cut-off grades over the LOM. The model, code-named 'NPVMining', uses realistic grade-tonnage realizations and commodity price distribution to account for uncertainty. NPVMining was applied to a gold mine case study and produced an NPV ranging between 7% and 186% higher than NPVs from deterministic approaches, thus demonstrating improved project value from using stochastic optimization approaches.

A two-step approach to incorporate cut-off grade and stockpiling in oil sands mine planning optimization framework

Article

Mar 2019
COMPUT OPER RES

In achieving maximum benefit in oil sands mining, the time and sequence of removing ore, dyke material and waste from the final pit limit is essential to the long-term production schedule. In-pit waste management strategy requires the simultaneous construction of dykes with the advancement of mining operations. This paper seeks to determine: 1) the time and sequence for removal of ore, dyke material and waste to maximize Net Present Value (NPV); 2) the quantity of dyke material required for dyke construction to minimize construction costs; and 3) the impacts of stockpiling and stockpile reclamation with limited time duration. An Integrated Cut-Off Grade Optimization (ICOGO) model was used to generate an optimum cut-off grade policy and a schedule for mining ore and waste, as well as overburden, interburden and tailings coarse sand dyke materials in long-term production planning. Subsequently, a Mixed Integer Linear Goal Programming (MILGP) model was developed to generate a detailed production schedule for removal of ore, waste and dyke materials from the final pit limit. The cut-off grade profile and schedule generated by the ICOGO model are used as guides to define the grade constraints and production goals required by the MILGP model. The developed models feature stockpiling with limited duration for long-term production scheduling. The models were applied to an oil sands case study to maximize the NPV of the operation. In comparison, whereas the ICOGO model solved the optimization problem faster, the MILGP model results provided detailed mining-cut extraction sequencing for practical mining.

A mathematical programming model for optimal cut-off grade policy in open pit mining operations with multiple processing streams

Article

Dec 2018

Cut-off grade classifies the available supply of ore (valuable) and waste material within a mineralised deposit. Given the mining, processing and refining limitations of a mining operation, an optimal cut-off grade policy ensures that the flow of ore from the mine to the processing and refining facilities is maintained at the maximum possible throughput. This policy defines a schedule of cut-off grades along with corresponding quantities of mineralised material to be mined, processed and metal refined in each period of the scheduling horizon. The criteria that controls the development of cut-off grade policy aligns with the strategic objectives of an operation in order to maximise the discounted value (net present value or NPV) over the life of operation. This paper proposes a new mixed integer linear programming (MILP) based model that maximises NPV subject to the mining, processing, refining capacity constraints and develops an optimal cut-off grade policy for an open pit mining operation with multiple processing streams. An implementation of the proposed method on hypothetical and realistic data promises a relatively higher NPV as compared to the traditional Lane’s approach practised in the mining industry

Application ofKKTindeterminingthe final destinationofmined materialinmulti-processingmines

Article

Aug 2016
RESOUR POLICY

Determining the final destinationofminedmaterialsiscountedasoneofthemostimportantchallenges in mining.Cut-offgradeisacriterionspecifyingthedestinationofminedmaterialsrelyingonthe commodity price,treatmentmethodrecovery,investmentandoperatingcosts. The developmentofmineralprocessingsciencemakesthesemethodsapplysimultaneouslyinmines, thus, itisneededtospecifymineralsdestination.Regardingenvironmentalandtechnicalconsiderations and operationcosts,theoptimumcut–off gradesofprocessingmethodsareestimated.Mineralsdesti- nation mightbechangedduetothedifferencesofinvestmentcostsofprocessingmethods.Optimization has beendonethroughtheKarush–Kuhn–Tucker(KKT)theoreminthisstudy.Thus,wetriedtoinnovate a novelalgorithmincoppermine.ResultsindicatedthatapplyingKKTtheoremcanincreasethemining NPV by5%ratherthantraditionalapproachofdeterminingcut-offgrades.Itisalsodemonstratedthat processing recoveryandoperatingandinvestingcostsaffectcut-offgrades.

A Cut-off Grade Optimization Model in Multi Product Open Pit Mining Considering Reclamation and Valuable Waste Materials

Article

Full-text available

Mar 2021

The common problem found in the mining company is how to determine the cut-off grade for the classification of ore and waste. The cut-off grade will greatly affect the revenues and costs of the mining companies. In this study, we develop cut-off grade optimization model by considering multi product and environmental factor such as reclamation and revaluing of waste materials. Multi product was chosen because most of the mining industry not only produce one type of mineral products. The main goal of this study is to develop a cut-off grade model to maximize the net present value (NPV). To illustrate the application of the model, the numerical example is given for mining case using the available data of Golgohar Iron Mine in Iran which produced three types of iron products, such as concentrated, sizing, and pellet.

Mining Method Selection for the Synclinorium Mining Project: A Case Study of Mopani Copper Mines, Zambia

Conference Paper

Full-text available

Apr 2019

Mining method selection is one of the most critical activities of mining engineering with the ultimate goal of maximizing profit, mineral recovery and arrive at a method with the least problems among feasible alternatives. The geology at the Synclinorium is complex with four main lithologies. A critical geological feature is the foliation or bedding that replicate the folding along the strike of the orebody. This poses a challenge in terms of selecting a suitable mining method for this orebody that will be less costly with high recoveries and low dilution. The main aims of the research were to select a suitable mining method, identify the current challenges encountered in the existing mining methods and carry out an economic evaluation of the Synclinorium mining project. The methodology used in data collection involved underground visits to various sections of the mine to understand the geology, rock types, orientations and geological discontinuities, current mining methods and associated challenges. The results gathered were then subjected to mine design criteria for selecting a mining method. In this research, University of British Colombia (UBC) mining method selection criteria was used for the selection of a suitable mining method. Both methods revealed that, Sublevel stoping, Cut and fill, Sublevel caving and Block caving were selected in that order. However, after subjecting the selected mining methods to geotechnical, technical and economic evaluation, Sublevel Open (SLOs) stoping with fill in the anticline, Sublevel caving (SLC) in the limbs and VCR in the synclines were recommended. The current SLC and Vertical Crater Retreat methods require modification to address the current challenges due to hang-ups, delayed hangingwall exposure and creation of a huge void prior to hangingwall collapse as mining progresses and hole deviations in VCR at 50m that results in redrilling and ultimately increase the costs of mining. The economic evaluation indicates that the Synclinorium mining project is viable with a projected average annual income of US$350 million.

Cut-off grade optimisation encompassing mineral royalty

Conference Paper

Full-text available

Apr 2019

Cut-off grade optimisation is an important step in any production planning setting. Being cognizant of this fact, it is imperative that this parameter be optimised. One of the earliest applied method of determining the optimal cut-off grade is the Lane algorithm. In this paper the Lane algorithm has been modified to encompass ad valorem mineral royalty. This is done with the objective of exhuming the relationship between the rate of ad valorem mineral royalty and optimal cut-off grade using the profit function. Results show that encompassing mineral royalty in the Lane algorithm increases the cut-off grade and reduces the total achievable profit of a mining project. Additionally, results show that there is a positive linear relationship between the ad valorem mineral royalty rate and optimal cut-off grade.

Influence of Sub-Grade Ores on the Cut-Off Grade and Ore Reserve of Itakpe Iron Ore Deposit, North-Central, Nigeria

Article

Full-text available

Apr 2020

Itakpe iron ore deposit is a multi-grade ore deposit with ore grades varying from 14.8%Fe to 41%Fe in the 25 ore layers. At the point of design of the mine, several low grade ores were deposited in temporary stockpile and a mineable ore reserve of 145mt was established. This paper examines the cut-off grade of Itakpe deposit in view of the current cost of mining, processing and waste removal. It further examines which of the low grade ores in temporary stockpile can now be included in the main ore reserve if the cost of their removal is considered as a credit towards the reduction of the cost of production. Analysis shows that the cut-off grade of Itakpe iron ore deposit without considering the ores currently in temporary stockpile is 26%Fe. It however lowers from 26%Fe to 23%Fe if the cost of production and value of some low grade ores are considered. The resultant effect is that ore reserve increases from 150mt for 26%Fe cut-off grade to 159mt for the cut-off grade of 23%Fe. Thus it becomes justifiable to send the additional 9 million tons whose grades vary from 26%Fe to 23%Fe to the mill especially considering the country’s need of iron ore concentrate for steel sector development. Keywords: Sub-grade ore, main ore reserve, cut-off grade, value per ton of ore, production cost per ton of ore.

Computer-Aided Cut-off Grade Optimisation for Open Pit Mines using Lane's Approach

Article

Full-text available

Dec 2018

A mine planning team is tasked among other duties with designing a feasible mine plan which in turn maps out the daily running of the mining project. A mine plan revolves around a cut-off grade which is thoughtfully and uniquely selected while considering various aspects such as grade tonnage distribution, economic and operational parameters specific to a mine. Selection of a cut-off grade can be a daunting task often involving iterative and lengthy mathematical formulas which take huge amounts of time to execute, often leaving room for error. In the occurrence of such errors, a mining project can be faced with sequential outcomes that could even lead to premature closure. The cut-off grade is therefore a strategic variable that determines the economic viability of a mine, and hence return on investment. It is critical that the cut-off grade is optimal so as to maximise the net present value. Lane’s approach is a model that utilises several steps to yield one cut-off grade value. This algorithm is flexible and can be adjusted to include other factors specific to a mine. Regrettably, many mining companies continue to operate using inaccurate cut-off grades wrongly calculated or assumed. This has continuously led to frustrations due to losses and prematurely abandoned mines. This study focused on the development and implementation of an easy to use computer application based on Lane’s approach that runs on Windows platform, and hence targeting a larger user base for choosing an optimum cut-off grade for open pit mines.

A New Methodology Based on Hill of Value for Ore Reserve Selection in Long-Term Planning for Block Caving

Article

Full-text available

Dec 2019

The underground mining evolution for block cave mines in Chile and worldwide has made important strides in the last decades. Nonetheless, reserves determination in the initial stages of these types of projects—mainly for long-term planning—is not studied in as much detail as it should be, especially regarding the impact on the final value of the enterprise. Today, the first estimation of the size of a block cave mine, typically expressed in tons, tends to determine very large footprints and ore bodies. The resulting large-scale mine is obtained by applying the marginal cut-off grade (COG) to determine reserves. Yet, in many cases, it is possible to obtain an equal or higher benefit, extracting fewer reserves in less time, with a smaller active area, which significantly reduces the project’s uncertainty. To explore scenarios obtained by applying a higher marginal COG in the initial phases of the project, the Hill of Value methodology is used to estimate the net present value (NPV) in relation to the production rate and the COG. However, the application of this methodology considers certain simplifications that generate results which are not completely satisfactory in specific cases. This paper suggests an improvement of this method to obtain more reliable results regarding determination of a COG profile that will optimize the NPV of a block-cave project. The methodology was developed and applied in a massive polymetallic deposit with zinc, lead, and silver mineralization, corresponding to a real block caving project. The methodology provides NPV results that differ by approximately 15% in comparison to the real mine plan, while also being considerably simpler and faster to calculate. In summary, the proposed methodology provides a reasonable and fast procedure to estimate higher than marginal COG that increases the NPV of block cave mine projects.

Review of Mathematical Models Applied in Open-Pit Mining

Chapter

Full-text available

Jan 2020

J. Githiria

Mining is the art of extraction of material from the earth surface for profit. The main objective of mining companies is to maximize net present value (NPV) while considering health, safety and environmental issues. Revolution in the mining industry has seen mathematical modelling being the key component in improving the mining process. Mining models has been proven as the next frontier that needs all the focus it can get. There are three mining stages namely: mining or extraction, processing and refining involved in this exercise. The major optimisation problems found in surface mining operations are ultimate pit limit problem, cut-off grade optimisation and open pit production scheduling. In order to maximise the output from the three mining stages, there is need to apply mathematical equations and models to optimise the whole process. There are extensive research studies since 1960s on development of mathematical models optimising mining operations. However, the mining industry has not fully appreciated and applied all these optimisation models. This paper highlights the strides made in development of mathematical models in the mining industry and their application. It discusses ways in which the mining industry can increase the application of these models to improve the output generated from the mining projects.

A Sequential Optimization Model of Cut-off Grade and Project/Location Selection in Open Pit Mining

Article

Full-text available

Sep 2019

Optimization of the cut-off grade for underground polymetallic mines

Article

Jan 2019
GOSPOD SUROWCAMI MIN

One of the most critical aspects of mine design is to determine the optimum cut-off grade. Despite Lane’s theory, which aims to optimize the cut-off grade by maximizing the net present value (NPV), which is now an accepted principle used in open pit planning studies, it is less developed and applied in optimizing the cut-off grade for underground polymetallic mines than open pit mines, as optimization in underground polymetallic mines is more difficult. Since there is a similar potential for optimization between open pit mines and underground mines, this paper extends the utilization of Lane’s theory and proposes an optimization model of the cut-off grade applied to combined mining-mineral processing in underground mines with multi-metals. With the help of 3D visualization model of deposits and using the equivalent factors, the objective function is expressed as one variable function of the cut-off grade. Then, the curves of increment in present value versus the cut-off grade concerning different constraints of production capacities are constructed respectively, and the reasonable cut--off grade corresponding to each constraint is calculated by using the golden section search method. The defined criterion for the global optimization of the cut-off grade is determined by maximizing the overall marginal economics. An underground polymetallic copper deposit in Tibet is taken as an example to validate the proposed model in the case study. The results show that the overall optimum equivalent cut-off grade, 0.28%, improves NPV by RMB 170.2 million in comparison with the cut-off grade policy currently used. Thus, the application of the optimization model is conducive to achieving more satisfactory economic benefits under the premise of the rational utilization of mineral resources.

Generic approach to developing an algorithm for mining related problems

Conference Paper

Full-text available

Sep 2018

Developing an algorithm is the first step when coming up with a mathematical model to optimise mining operations. An algorithm is a systematic procedure to accomplish a specific task. It is the idea behind any reasonable computer program. Mining has come to a stage where mine planners have embraced optimisation in planning their operations. Mine planning for any operation (surface or underground) is aimed at maximising the value realized from the orebody. Consequently, most mines use computer-programming tools to optimise the ore extraction processes. The challenge faced by researchers in the mining industry when solving mining related problems is in the design of algorithms that solve problems accurately, fast and efficient. These algorithms need to apply to real mining environments. Hence, this paper provides a guideline to be employed when developing an algorithm for mining related problems. There is no one process to develop an algorithm due to the uniqueness of the orebody setting environments, however, the material presented in this paper provides generic thought-processes.

A Cut-Off Grade Optimization Model in Open Pit Mining Considering Reclamation Cost and Revenue

Article

Full-text available

Mar 2021

In open pit mining industry, cut-off grade has an important roles in affecting the total profit that will be earned by the company. In this research, cut-off grade optimization model is developed for open pit mining industry to maximize the total profit. We consider the environmental aspect in this model which consists of reclamation cost and reclamation revenue. We also consider the revenue of sales and valuable wasted materials revenue, and also the cost of selling stage, processing cost, mining cost, waste removal/rehabilitation cost and fixed cost. The results show that the model is able to determine the optimal cut-off grade and total profit that will be earned by the company can be estimated. Besides that, we can also estimate the completion time of mining project and the value of Net Present Value (NPV) and Return on Investment (ROI). The application of the model can be illustrated using numerical example that given in this study.

Open-pit mining complex optimization under uncertainty with integrated cut-off grade based destination policies

Article

Nov 2020
RESOUR POLICY

The aim of a mining complex optimization is to maximize the economic value of the mining project as a whole. To maximize the economic value, it is required to simultaneously optimize the mining extraction sequence and destination of the material into various processing streams. This work presents a global optimization model to simultaneously optimize all aspects of the mining complex under uncertainty. To solve the mining complex problem, the method uses a combination of the maximum flow and a genetic algorithm to define the optimal production sequence, and the flow of extracted material into various destination streams are defined based on the dynamic cutoff grade optimization and block economic values. The dynamic cutoff grade is optimized using Lane's method. An application for a copper-gold mining complex indicates that the optimizer generates results that reduce the risk of not meeting the targets. When compared to commercial deterministic mine planning software, proposed algorithm generates 9.08% higher net present value and the stochastic design generated 13.70% higher expected net present value compared. Two different destination policies are evaluated to study the impact of destination policies on the net present value. Due to change in destination policies, difference of 4.36% is observed in net present value for the stochastic model.

Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-Integer Programming Approach

Article

Aug 2020

Production scheduling is a large-scale optimization problem that must be solved on a yearly basis by every open pit mining project throughout the world. Surprisingly, however, this problem has only recently started to receive much attention from the operations research community. In this article, O. Rivera, D. Espinoza, M. Goycoolea, E. Moreno, and G. Muñoz propose an integer programming methodology for tackling this problem that combines new classes of preprocessing schemes, cutting planes, heuristics, and branching mechanisms. This methodology is shown to compute near-optimal solutions on a number of real-world planning problems whose complexity is beyond the capabilities of preexisting approaches.

A Multi-Objective Optimization Model Using Improved NSGA-II for Optimizing Metal Mines Production Process

Article

Full-text available

Feb 2020

Production process optimization is an indispensable step in industrial production. The optimization of the metal mines production process (MMPP) can increase production efficiency and thus promote the utilization rate of the metal mineral resources in the frame work of sustainable development. This study establishes a multi-objective optimization model for optimizing the MMPP by maximizing economic and resource benefits. To get better non-dominated Pareto optimal solutions, an improved non-dominated sorting genetic algorithm-II (NSGA-II) is proposed. The symmetric Latin hypercube design is adopted to generate the initial population with high diversity. The mutation and crossover of the differential evolution algorithms are introduced into the NSGA-II to replace the genetic algorithm for improving convergence. The control parameters of the mutation scale factor and crossover rate of the differential evolution algorithm are adaptively adjusted to improve the diversity of candidate solutions. To verify the performance of the improved NSGA-II, four test functions from the ZDT series functions are chosen for experimentation. The experimental results indicate that the improved NSGA-II outperforms the comparative algorithms in diversity and convergence. Moreover, the application of the proposed method to the Yinshan copper mines shows that the improved NSGA-II is effective in optimizing the MMPP and a reliable method in promoting utilization rate of metal mineral resources in the framework of sustainable development.

Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming

Article

Jun 2020
RESOUR POLICY

In the process of planning an open-pit, the determination of optimum cutoff grade plays a vital role. The classical approach of Lane's algorithm yields infinitely many solutions when the metal price is very high and mining, milling and refining costs are low. This problem has been addressed through a new algorithm. This study deals with the optimization of cutoff grade of a real-life case study of an open-pit copper mine in India considering fixed annual production of mine, mill and refinery facilities. However, the optimization ignores uncertainty in input parameters. The optimization has been carried out with the objective of maximizing the discounted total profit in terms of Net Present Value (NPV). As the process of determination of optimum cutoff grade of the deposit is dependent on many parameters which can suitably be addressed using a linearly advancing algorithm derived from dynamic programming approach. Considering a precision of 0.01% in the grade interval, the optimum cutoff grades, the amount of metal produced per ton and the NPV have been evaluated. Accordingly, the optimum cutoff grade of the Malanjkhand copper deposit has been found to be 0.32% amounting to a maximum NPV of ₹ 12123 million. The calculation reveals that the life of mine is 37.5 years and the average mill head grade optimises to 1.12%. The results also reveal that the present value of net cash-flow increases in the initial years, reaches a maximum value at a certain mid-life time and then declines with the depletion of the reserve. The NPV finally reaches a zero value at the end of mine life corroborating the general trend as seen in other mining organisations.

Economic potential of new ore products in processing plant operations: A case study from midsize prospects, Atacama Chile

Article

Jan 2019

This paper proposes a methodology to evaluate the economic potential of mining prospects with a 'multi-product' approach. The National Mining Company (ENAMI) is a Chilean producer traditionally engaged in copper, silver and gold production and commercialization. Using this methodology it has been possible to identify other commodities with greater geological, market and technological potential. Prospects studied were valued using economic-mining criteria such as the cut-off grade, marginal cut-off grade and equivalent grade. In this work, thirteen commodities were analyzed and seven of them stand out: molybdenum, lithium, iron, bismuth, tungsten, rare earths (REE) and titanium. For every commodity, it is essential to know the geological characteristics of the prospect, the mining and processing technologies, the purchase point closest to the prospect and the market for these commodities. The sources of information are public bodies specialized in these matters, such as the National Geology and Mining Service, SERNAGEOMIN; the Chilean Copper Commission, COCHILCO. Sixteen ENAMI prospects were valued based on the proposed methodology and six of them presented the greatest economic potential: Salado Norte, Cerro Negro, Pazota, Pastenes, Laura–Laurita and Carmen Sur

Lessons from Some Recent and Current Mine Planning Related Postgraduate Research Work at the University of the Witwatersrand

Chapter

Jan 2019

C. Musingwini

A method for optimal cut-off grade policy in open pit mining operations under uncertain supply

Article

Jan 2019
RESOUR POLICY

Cut-off grade controls the movement of materials among mining, processing and refining stages of an open pit mining operation. The cut-off grade policy constitutes a schedule of cut-off grades and the associated quantities of materials that flow through various stages over the life of operation. This flow of materials in the system relies on the grade-tonnage curve of the mineral resource and given that the variation in grade-tonnage curve is inevitable, it is crucial that the methods that define the cut-off grade policy must consider this grade uncertainty. However, with few exceptions, a majority of these methods ignore this uncertainty in the supply of materials. This paper shares a two-stage stochastic linear programming based cut-off grade optimisation model that accounts for the grade uncertainty and maximises the net present value (NPV) subject to the production capacity constraints over the life of operation. An application of the proposed method at hypothetical and realistic cases promises higher NPV as compared to the traditional heuristic approach.

Cutoff grades optimization in open pit mines using meta-heuristic algorithms

Article

Mar 2019
RESOUR POLICY

To have a sound production planning one of the main factors that should be considered is the cutoff grade. The cutoff grade is used as a criterion to identify waste of minerals in a mining reserve. The cutoff grade is one of the most sensitive parameters that can have a significant impact on net present value (NPV) and cash flow of projects. Since the cutoff grade has a significant impact on the operation, the choice of the correct level of this grade is of considerable importance. Choosing the optimal cutoff grade maximizes the NPV and the total profit of the mining operation and the project. The optimization of the cutoff grades considering the maximum achievable NPV over the life of the mine is one of the key issues in the mining of open pits. In this paper, two different meta-heuristic optimization algorithms are employed to determine the optimal cutoff grade. For this purpose, taking into account the precision of 0.001%, the optimum cutoff grades, the production amount of each unit and the NPV are calculated. Accordingly, the optimum cutoff grades of iron mine No. 1 Golgohar was obtained using the PSO algorithm is 49.11-40.6%, and using the imperialist competitive algorithm, the optimum cutoff grades of iron mine No. 1 Golgohar was obtained from 48.56% to 40.5%. The results show that the determination of the cutoff grade by using these two methods has high accuracy and speed. According to the results, the ICA algorithm has a higher accuracy than the PSO algorithm.

YPC paper 19th Sept 2018

Conference Paper

Sep 2018

Developing an algorithm is the first step when coming up with a mathematical model to optimise mining operations. An algorithm is a systematic procedure to accomplish a specific task. It is the idea behind any reasonable computer program. Mining has come to a stage where mine planners have embraced optimisation in planning their operations. Mine planning for any operation (surface or underground) is aimed at maximising the value realized from the orebody. Consequently, most mines use computer-programming tools to optimise the ore extraction processes. The challenge faced by researchers in the mining industry when solving mining related problems is in the design of algorithms that solve problems accurately, fast and efficient. These algorithms need to apply to real mining environments. Hence, this paper provides a guideline to be employed when developing an algorithm for mining related problems. There is no one process to develop an algorithm due to the uniqueness of the orebody setting environments, however, the material presented in this paper provides generic thought-processes.

Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit

Article

Full-text available

Jun 2018

An integral connection exists among the mine production planning, the mined material destination, and the ultimate pit limit (UPL) in the mining engineering economy. This relation is reinforced by real information and the benefits it engenders in the mining economy. Hence, it is important to create optimizing algorithms to reduce the errors of economic calculations. In this work, a logical mathematical algorithm that considers the important designing parameters and the mining economy is proposed. This algorithm creates an optimizing repetitive process among different designing constituents and directs them into the maximum amount of the mine economical parameters. This process will produce the highest amount of ores and the highest degree of safety. The modeling produces a new relation between the concept of the cutoff grade, mine designing, and mine planning, and it provides the maximum benefit by calculating the destination of the ores. The proposed algorithm is evaluated in a real case study. The results show that the net present value of the mine production is increased by 3% compared to previous methods of production design and UPL.

Integrated stochastic optimization of stope design and long-term underground mine production scheduling

Article

Full-text available

Sep 2022
RESOUR POLICY

In the commonly used underground mine planning framework, mine design is first established and is the main input for the subsequent long-term mine production scheduling optimization. This sequential optimization approach cannot, therefore, capture the synergies between the involved planning steps, generating solutions that depart substantially from a global optimum. In addition, traditional underground mine planning methods for stope design and life-of-mine production scheduling are deterministic and are based on a single estimated orebody model. As a result, the uncertainty and variability in grades and material types are not incorporated into the optimization process, resulting in designs that misrepresent all high-, medium- and low-grade stoping volumes and production schedules with misleading forecasts. A two-stage stochastic integer program (SIP) for integrated optimization of stope and development network designs and an underground mine production scheduling are proposed for the sublevel open stoping mining method under grade uncertainty and variability, quantified by a set of geostatistical simulations of the mineral deposit considered. Assuming a mine is accessed through a shaft, the model defines a schedule of levels and stopes, which aims to maximize the discounted revenues, minimize development costs, and manage the risk of not meeting production targets, while satisfying geotechnical constraints. The practical aspects of the proposed method are presented through an application at an underground gold mine. A comparison with the stepwise framework, where the stope design is input to a subsequent optimization of the production schedule, shows that the proposed approach provides a physically different design and production schedule with an 11% higher net present value (NPV) and a life-of-mine that is two years shorter, affirming the advantages of the integrated optimization process.

Advanced Analytics for Dynamic Programming

Chapter

Feb 2022

In open-pit mine planning, the determination of optimum cut-off grade is essential for the mine designing process. Selection of the optimum cut-off grade maximizes the net present value (NPV) of an open-pit mining operation subject to the variable mining capacities, milling, smelting, and refining. The cut-off grade of a metalliferous deposit is dynamic; thus, the dynamic programming approach may be considered one of the suitable methods for solving the cut-off grade determination problem. This chapter analyzes cut-off grade optimization of an open-pit copper mine project considering fixed annual mine, mill, and refinery production. A computer-driven model, namely the cut-off grade optimizer (COGO) derived from a dynamic programming algorithm built-in Visual Basic using C programming language, has been developed. The cut-off grade planner (COGP) software package developed in the present research comprises three modules—input data module, output result module, and graphical module. The algorithm and the associated software have been validated using a portion of the data of the Sarcheshmeh copper mine from a published paper. The results of the analysis are encouraging. The optimum cut-off grade of the copper deposit has been determined to be 0.24% resulting in a maximum NPV of $83,714 million, with an optimized mine life of 23.5 years, and the average mill head grade corresponds to 0.707%.KeywordsDynamic programmingCut-off gradeRefiningOptimizationMining

Mining Geometrical Modelling Approach for the Estimation of Cut-Off Grade of Open-Pit Mines, Through Maximization of the Net Present Value

Article

Full-text available

Dec 2021

Jmg Nmgs

The theory of cut-off grade estimation has taken a new dimension since Lane's proposal of maximum net present value criterion for cut-off grade estimation. However, whereas this criterion is widely accepted by mine planners, Lane's analytical method of its realisation has been subjected to several criticisms. In this paper a geometrical modelling approach has been proposed for realisation of the maximum net present criterion which overcomes the shortfalls of Lane's analytical approach. This geometrical modelling approach was applied to a hypothetical deposit with five ore bodies of varying grades. The approach is applicable to situations of varying production rates, costs of production and prices and can be utilised when multiple processing streams are available.

Analysis of the discount rate for mining projects

Conference Paper

Full-text available

Jan 2020

Alfonso Ovalle

A novel cut-off grade method for increasing the sustainability of underground metalliferous mining operations

Article

Oct 2021
MINER ENG

The determination of a cut-off grade is considered to be one of the main steps in the design and strategic planning of mining operations. This is due to its role in distinguishing between waste material and valuable ore. This becomes increasingly important as the mining industry is facing lower grades within an uncertain market. The implementation of pre-concentration systems prior to main processing has significant potential to increase the sustainability and resource utilisation of mining operations, which can result in the reduction of mine cut-off grade. This paper reviews the technical concepts of integration of pre-concentration systems into underground mines and presents a novel method for underground cut-off grade calculation. The proposed model is implemented on a sublevel stoping operation to illustrate the impacts and advantages of the underground pre-concentration integration. The outputs of this study and investigation of various scenarios prove an increase in the profitability, efficiency and sustainability of the underground operations.

Principles of Surface Mining of Mineral Deposits

Chapter

Jan 2022

A classification of mineral deposits is illustrated in Fig. 2.1.This indicates the influence of the shape of a deposit on the design work. In general, stratified deposits are in softer, younger sedimentary rocks and non-stratified are in harder, older, igneous rocks

Mine Planning and the Crucial Role of Geology

Article

Jul 2019

Editor’s note: The Geology and Mining series, edited by Dan Wood and Jeffrey Hedenquist, is designed to introduce early-career professionals and students to a variety of topics in mineral exploration, development, and mining, in order to provide insight into the many ways in which geoscientists contribute to the mineral industry. Abstract Mine planning is the process that determines the way in which an ore deposit will be mined over the life of a mining operation. It necessarily draws on everything that planning engineers believe will determine the ultimate success of the proposed mine and uses as its foundation all of the geology-related data on the deposit. It is both a strategic and a tactical process that first considers a longer-term horizon based on strategic considerations, followed by more detailed shorter-term planning processes, in this order; the latter are the result of tactical considerations. This structured process may also be referred to as integrated mine planning, and it is driven by a broader corporate strategy or set of objectives. As such, it is much more than the mining engineering section of the mine development process. It has to include inputs from all related disciplines, by combining all of the measured properties of the deposit with mining-associated parameters. This results in the planning process incorporating a significant number of interrelated parameters. If these parameters are not used diligently and accurately or are not well aligned, or if the underlying data are deficient in either quantity or quality, the project or operation is unlikely to achieve its potential, by virtue of failures in the planning process. Best-practice integrated planning incorporates relevant inputs from all mining-related fields: geology, geotechnical, geochemical, hydrogeological, hydrology, mining operations, minerals processing, marketing of product, waste management, tailings, environmental, social science, mine closure, etc. It includes all interfaces in the business-value driver model, from exploration drill holes to the mine closure plan. The planning process cannot be completed successfully by mining engineers working in isolation from professionals in other key disciplines. Because geology provides the foundation on which the mine plan is built, the quality and accuracy of the geologic data provided to planning teams by exploration geoscientists is crucial.

A New Mathematical Formulation for Underground Cut-off Grade Determination in the Presence of Pre-concentration Systems

Article

Jun 2021

The mining industry is facing increasingly lower grades, which intensifies the need to reduce costs. The depletion of orebodies close to the surface has pushed the mining industry to progressively explore and extract deposits through underground mining. One approach that is receiving more attention is the application of pre-concentration systems prior to introducing the extracted materials to the main processing plant. Integration of pre-concentration systems into mining operations particularly in underground mines can significantly increase the sustainability and efficiency of operations. This paper reviews the technical concepts of this integration and presents a new mathematical formulation for underground cut-off grade determination, which should play an important role in resource utilisation and strategic planning in any operation. The proposed formulation is implemented on an underground operation to illustrate the impacts and advantages of underground pre-concentration integration. The outputs of this study prove the economic potential of pre-concentration systems in reduction in cut-off grade and increasing NPV.

Mining Geometrical Modelling Approach for the Estimation of Cut-Off Grade of Open-Pit Mines, Through Maximization of the Net Present Value

Article

Full-text available

Apr 2021

The theory of cut-off grade estimation has taken a new dimension since Lane's proposal of maximum net present value criterion for cut-off grade estimation. However, whereas this criterion is widely accepted by mine planners, Lane's analytical method of its realisation has been subjected to several criticisms. In this paper a geometrical modelling approach has been proposed for realisation of the maximum net present criterion which overcomes the shortfalls of Lane's analytical approach. This geometrical modelling approach was applied to a hypothetical deposit with five ore bodies of varying grades. The approach is applicable to situations of varying production rates, costs of production and prices and can be utilised when multiple processing streams are available.

A mathematical model for open pit mine production scheduling with Grade Engineering and stockpiling

Article

Apr 2021

This paper presents the development and implementation of an innovative mixed integer programming based mathematical model for an open pit mining operation with Grade Engineering framework. Grade Engineering comprises a range of coarse-separation based pre-processing techniques that separate the desirable (i.e., high-grade material) and undesirable (i.e., low-grade or uneconomic) materials and ensure the delivery of only selected quantity of high quality (or high-grade) material to energy, water and cost-intensive processing plant. The model maximizes the net present value under a range of operational and processing constraints. Given that the proposed model is computationally complex, the authors employ a data pre-processing procedure and then evaluate the performance of the model at several practical instances using computation time, optimality gap and the net present value as valid measures. In addition, a comparison of the proposed and traditional (without Grade Engineering) models reflects that the proposed model outperforms the traditional formulation.

Review of Solution Methodologies for Open Pit Mine Production Scheduling Problem

Article

Jan 2020

The open pit mine production scheduling problem determines a sequence of three-dimensional, notional block extraction that maximizes net present value (NPV) of future cash flows and satisfies technical and operational constraints such as precedence between blocks and resource availability. Since the 1960s, researchers have developed a variety of mathematical models that address block extraction at the strategic, tactical and operational levels, and the complexities associated therewith, e.g., risk and uncertainty, inventory strategies, environmental concerns and downstream processing. Given that these mathematical models are computationally complex, i.e., they are generally categorized as NP hard, a significant portion of the literature is dedicated to the development and performance of solution approaches spanning from exact and heuristics to recent meta-heuristic methods. This paper provides a comprehensive overview of recent contributions (from 2012 to early 2019) and discusses proposed future studies.

Choosing the optimum cut-off grade

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